Preprints Physics

Authors: Ievgen Dubovyk, Ayres Freitas, Janusz Gluza, Krzysztof Grzanka, Martijn Hidding, and Johann Usovitsch

Preprint number: UUITP-66/21

Abstract: Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders will require three-loop electroweak and mixed electroweak-QCD corrections to single-particle production and decay processes and two-loop electroweak corrections to pair production processes, all of which are beyond the reach of existing analytical and numerical techniques in their current form. This article presents a new semi-numerical approach based on differential equations with boundary terms specified at Euclidean kinematic points. These Euclidean boundary terms can be computed numerically with high accuracy using sector decomposition or other numerical methods. They are then mapped to the physical kinematic configuration with a series solution of the differential equation system. The method is able to deliver 8 or more digits precision, and it has a built-in mechanism for checking the accuracy of the obtained results. Its efficacy is illustrated with examples for three-loop self-energy and vertex integrals and two-loop box integrals.

Authors: Agnese Bissi, Francesco Fucito, Andrea Manenti, Francisco Morales, Raffaele Savelli

Preprint number: UUITP-65/21

Abstract: The calculation of physical quantities in certain quantum field theories such as those of the Argyres-Douglas type is notoriously hard, due to the lack of a Lagrangian description. Here we tackle this problem following two alternative approaches. On the one hand, we use localization on the four-sphere to compute two-correlators and OPE coefficients in Argyres-Douglas superconformal theories. On the other hand, we use the conformal bootstrap machinery to put stringent bounds on such coefficients, only relying on the knowledge of central charge and conformal dimension of the operators. We compare the results obtained with these two methods and find good agreement for all rank-one cases and for the rank-two Argyres-Douglas theories $(A_1,A_4)$ and $(A_1,A_5)$, in the moduli space of pure $SU(5)$ and $SU(6)$ super Yang-Mills. We also apply our results from localization to obtain bounds on the dimensions of the lightest neutral unprotected operators of the CFTs.

Authors: Roman Mauch and Lorenzo Ruggeri

Preprint number: UUITP-64/21

Abstract: In this note we present a formula for the equivariant index of the cohomological complex obtained from localization of N=2 SYM on simply-connected compact four-manifolds with a T²-action. Knowledge of said index is essential to compute the perturbative part of the partition function for the theory. In the topologically twisted case, the complex is elliptic and its index can be computed in a standard way using the Atiyah-Bott localization formula. Recently, a framework for more general types of twisting, so-called cohomological twisting, was introduced for which the complex turns out to be only transversally elliptic. While the index of such a complex has been computed for some cases where the manifold can be lifted to a Sasakian S¹-fibration in five dimensions, a general four-dimensional treatment was still lacking. We provide a formal, purely four-dimensional treatment of the cohomological complex, showing that the Laplacian part can be globally split off while the remaining part can be trivialized uniquely in the group-direction. This ultimately produces a simple formula for the index applicable for any compact simply-connected four-manifold. Finally, the index formula is applied to examples on S⁴, CP² and F¹. For the latter, we use the result to compute the perturbative partition function.

Authors: Maor Ben-Shahar,  Henrik Johansson

Preprint number: UUITP-63/21

Authors: John Joseph Carrasco,  Alexander Edison,  Henrik Johansson

Preprint number: UUITP-62/21

Abstract: We construct the complete (planar and non-planar) integrand for the six-loop four-point amplitude in maximal D=<10 super-Yang-Mills. This construction employs new advances that combat the proliferation of diagram contributions and state sums when evaluating multi-loop D-dimensional unitarity cuts.  Concretely, we introduce two graph-based approaches to evaluating generalized unitarity cuts in D dimensions: 1) recursively from lower-loop cuts, or 2) directly from known higher-loop planar cuts. Neither method relies on explicit state sums or any sewing of tree-level amplitudes.  These methods are based on identities that we expect to hold for a broad family of theories, including  QCD and Einstein gravity.

Authors: Jung-Wook Kim, Michèle Levi, Zhewei Yin

Preprint number: UUITP-61/21

Abstract: We derive the observable binding energies and their relations to the angular momentum for the next-to-next-to-next-to-leading order (N^3LO) of all quadratic-in-spin interactions in post-Newtonian (PN) gravity. Our results are valid for all generic compact binaries, and enter at the fifth PN order for maximally-rotating compact objects, thus pushing the state of the art. This is accomplished through an extension of the effective field theory of spinning gravitating objects. We find a new operator that contributes to the observables, making the associated Wilson coefficient a new probe for candidate theories of gravity and for QCD.

Authors: Andreas Brandhuber, Gang Chen, Henrik Johansson, Gabriele Travaglini and Congkao Wen

Preprint Number: UUITP-60/21

Abstract: We present a closed formula for all BCJ numerators describing D-dimensional tree-level scattering amplitudes in a heavy-mass effective field theory with two massive particles and an arbitrary number of gluons. The corresponding gravitational amplitudes obtained via the double copy directly enter the computation of black-hole scattering and gravitational-wave emission. Our construction is based on finding a kinematic algebra for the numerators, which we relate to a quasi-shuffle Hopf algebra. The BCJ numerators thus obtained have a compact form and intriguing features: gauge invariance is manifest, locality is respected for massless exchange, and they contain poles corresponding to massive exchange. Counting the number of terms in a BCJ numerator for n-2 gluons gives the Fubini numbers F_{n-3} reflecting the underlying quasi-shuffle Hopf algebra structure. Finally, by considering an appropriate factorisation limit, the massive particles decouple, and we thus obtain a kinematic algebra and all tree-level BCJ numerators for D-dimensional pure Yang-Mills theory.

Authors: Vittorio Del Duca, Robin Marzucca, Bram Verbeek

Preprint Number: UUIPT-59/21

Abstract: We compute the three-loop leading-colour corrections to the Yang-Mills Regge trajectory and gluon impact factor. Conjecturing that, in analogy with N=4 super Yang-Mills (SYM), in a suitable scheme Nc-subleading terms are absent from the three-loop Regge trajectory, we understand our result as the first computation of the pure gauge, or nf = 0, part of the QCD three-loop Regge trajectory. The results are presented both for the bare and renormalised amplitudes and are consistent with predictions from infrared factorisation along with reproducing known results in planar N=4 SYM through a maximal weight truncation. We also include the dependence on a Regge factorisation scale to facilitate future applications in BFKL theory at next-to-next-to leading logarithmic accuracy.

Authors: Adam Chalabi, Christopher P. Herzog, Andy O'Bannon, Brandon Robinson, Jacopo Sisti

Preprint number: UUITP-58/21

Abstract: Motivated by questions about quantum information and classification of quantum field theories, we consider Conformal Field Theories (CFTs) in spacetime dimension d ≥ 5 with a conformally-invariant spatial boundary (BCFTs) or 4-dimensional conformal defect (DCFTs). We determine the boundary or defect contribution to the Weyl anomaly using the standard algorithm, which includes imposing Wess-Zumino consistency and fixing finite counterterms. These boundary/defect contributions are built from the intrinsic and extrinsic curvatures, as well as the pullback of the ambient CFT's Weyl tensor. For a co-dimension one boundary or defect (i.e. d=5), we reproduce the 9 parity-even terms found by Astaneh and Solodukhin, and we discover 3 parity-odd terms. For larger co-dimension, we find 23 parity-even terms and 6 parity-odd terms. The coefficient of each term defines a "central charge'' that characterizes the BCFT or DCFT. We show how several of the parity-even central charges enter physical observables, namely the displacement operator two-point function, the stress-tensor one-point function, and the universal part of the entanglement entropy. We compute several parity-even central charges in tractable examples:  monodromy and conical defects of free, massless scalars and Dirac fermions in d=6; probe branes in Anti-de Sitter (AdS) space dual to defects in CFTs with d ≥ 6; and Takayanagi's AdS/BCFT with d=5. We demonstrate that several of our examples obey the boundary/defect a-theorem, as expected.

Authors: N. Nekrasov, N. Piazzalunga, M. Zabzine

Preprint number: UUITP-57/21

Abstract: We study the dynamics of supersymmetric theories in five dimensions obtained by compactifications of M-theory on a Calabi-Yau threefold X. For a compact X, this is determined by the geometry of X, in particular the Kahler class dependence of the volume of X determines the effective couplings of vector multiplets. Rigid supersymmetry emerges in the limit of divergent volume, prompting the study of the structure of Duistermaat-Heckman formula and its generalizations for non-compact toric Kahler manifolds. Our main tool is the set of finite-difference equations obeyed by equivariant volumes and their quantum versions. We also discuss a physical application of these equations in the context of seven-dimensional gauge theories, extending and clarifying our previous results.

Authors: Finn Bjarne Kohl, Magdalena Larfors and  Paul-Konstantin Oehlmann

Preprint number: UUITP-56/21

Abstract: In this work we study F-theory on symmetric toroidal orbifolds that exhibit roto-translations, which are point group rotations accompanied by fractional lattice shifts.

These geometries admit a rich class of effects, such as twisted affine folded fibers, multiple fibers, and up to three distinct torus-fibrations that yield different M/F-theory lifts. We discuss the six-dimensional physics of the F-theory lifts, which generically host superconformal subsectors and a IIB axio-dilaton fixed to strong coupling. In addition we find that these theories exhibit a rich set of $p=0,1,2$ discrete $p$-form gauge symmetries. We discuss six-dimensional gauge and supergravity anomalies and match the rank and tensor branch dimension to the Hodge numbers that were computed using heterotic world sheet techniques.  

Authors: Agnese Bissi, Giulia Fardelli, Andrea Manenti

Preprint number: UUITP-55/21

Abstract: We start a systematic study of quarter-BPS operators in four-dimensional N = 4 Super Yang-Mills with gauge group SU(N) making use of recently developed tools in conformal field theory. We adapt the technology of embedding space tensor structures in four dimensions to the problem of computing R-symmetry tensor structures, and we use the underlined chiral algebra to obtain the superconformal Ward identities. This allows us to fix the protected part of the four-point correlators, up to few ambiguities. As applications, we use the Lorentzian inversion formula to study the leading order OPE data in the large N supergravity limit and we make contact with the OPE limit of the five-point function of half-BPS operators.

Authors: F. Bonechi, J. Qiu, M. Tarlini, E. Viviani

Preprint number: UUITP-54/21

Abstract: We discuss the diagonalization problem of the Nijenhuis tensor in a class of {\it Poisson-Nijenhuis} structures defined on compact hermitian symmetric spaces. We study its action on the ring of invariant polynomials of a Thimm chain of  subalgebras. The existence of $\phi$-{\it minimal representations} defines a suitable basis of invariant polynomials that completely solves the diagonalization problem. We prove that such reprentations exist in the classical cases AIII, BDI, DIII and CI, and do not exist in the exceptional cases EIII and EVII. We discuss a second general construction that in these two cases computes partially the spectrum and hints at a different behavior with respect to the classical cases.

Authors: Magdalena Larfors, Andre Lukas, Fabian Ruehle, Robin Schneider

Preprint number: UUITP-53/21

Abstract: We present a new machine learning library for computing metrics of string
compactification spaces. We benchmark the performance on Monte-Carlo sampled
integrals against previous numerical approximations and find that our neural
networks are more sample- and computation-efficient. We are the first to
provide the possibility to compute these metrics for arbitrary, user-specified
shape and size parameters of the compact space and observe a linear relation
between optimization of the partial differential equation we are training
against and vanishing Ricci curvature.

Authors: Jim Lundin and Lorenzo Ruggeri

Preprint number: UUITP-52/21

Abstract: We introduce a generic procedure to reduce a supersymmetric Yang-Mills (SYM) theory along the Hopf fiber of squashed $S^{2r-1}$ with $U(1)^r$ isometry, down to the $\mathbb{CP}^{r-1}$ base. This amounts to fixing a Killing vector $v$ generating a $U(1)\subset U(1)^r$ rotation and dimensionally reducing either along $v$ or along another direction contained in $U(1)^r$. To perform such reduction we introduce a $\mathbb{Z}_p$ quotient freely acting along one of the two fibers. For fixed $p$ the resulting manifolds $S^{2r-1}/\mathbb{Z}_p\equiv L^{2r-1}(p,\pm 1)$ are a higher dimensional generalization of lens spaces. In the large $p$ limit the fiber shrinks and effectively we find theories living on the base manifold. Starting from $\mathcal{N}=2$ SYM on $S^3$ and $\mathcal{N}=1$ SYM on $S^5$ we compute the partition functions on $L^{2r-1}(p,\pm 1)$ and, in the large $p$ limit, on $\mathbb{CP}^{r-1}$, respectively for $r=2$ and $r=3$. We show how the reductions along the two inequivalent fibers give rise to two distinct theories on the base. Reducing along $v$ gives an equivariant version of Donaldson-Witten theory while the other choice leads to a supersymmetric theory closely related to Pestun's theory on $S^4$. We use our technique to reproduce known results for $r=2$ and we provide new results for $r=3$. In particular we show how, at large $p$, the sum over fluxes on $\mathbb{CP}^2$ arises from a sum over flat connections on $L^{5}(p,\pm 1)$. Finally, for $r=3$, we also comment on the factorization of perturbative partition functions on non simply connected manifolds.

Authors: Luis F. Alday, Agnese Bissi,  Xinan Zhou

Preprint number: UUITP-51/21

Authors: Usman Naseer and Charles Thull

Preprint number: UUITP-50/21

Abstract: We study $\NN=2$ theories on four-dimensional manifolds that admit a Killing vector $v$ with isolated fixed points. It is possible to deform these theories by coupling position-dependent background fields to the flavor current multiplet. The partition function of the deformed theory only depends on the value of the background scalar fields at the fixed points of $v$. For a single adjoint hypermultiplet, the partition function becomes independent of the supergravity as well as the flavor background if the scalars attain special values at the fixed points. For these special values, supersymmetry at the fixed points enhances from the Donaldson-Witten twist to the Marcus twist or the  Vafa-Witten twist of $\NN=4$ SYM. Our results explain the recently observed squashing independence of $\NN=2^*$ theory on the squashed sphere and provide a new squashing independent point. Interpreted through the AGT-correspondence, this implies the $b$-independence of torus one-point functions of certain \emph{local} operators in Liouville/Toda CFT. The position-dependent deformations imply relations between correlators of partially integrated operators in \emph{any} $\NN=2$ SCFT with flavor symmetries.

Authors: Ulf Danielsson, Suvendu Giri

Preprint number: UUITP-49/21

Abstract: In arXiv:1705.10172 a string theory inspired alternative to gravitational collapse was proposed, consisting of a bubble of AdS space made up of ingredients from string theory. These ultra compact objects are 9/8 times the size of the corresponding Schwarzschild black hole, but being within the photosphere are almost indistinguishable from them. Slowly rotating counterparts of these black shells were constructed in arXiv:1712.00511, which closely mimic a Kerr black hole, but have a quadrupole moment that differs from Kerr. Recently, arXiv:2109.09814 studied the dynamicalstability of the stationary black shells against radial perturbations and accretion of matter, andexamined a two parameter family of fluxes required for stability. In this paper, we re-examine therotating black shells with particular attention to the constraints imposed by this dynamical analysisfor non-rotating shells. Extrapolating these results to rotating shells, we find that they can indeedsupport themselves at a critical point in the gravitational potential. Additionally, requiring that theysettle back to their new Buchdahl radius after accreting matter, uniquely fixes the fluxes required fordynamical stability. The flux parameters turn out to have an extremely simple form, and fulfil oneof the constraints for perturbative radial stability while exactly saturating the other. The preferredquadrupole moment that we find, given some physical assumptions, is 7% less than Kerr.

Authors: Ulf Lindström and Özgür Sariıoğlu

Preprint number: UUITP-48/21

Abstract: We discuss conserved currents constructed from the Cotton tensor and (conformal) Killing-Yano tensors. We consider the corresponding charges generally and then exemplify with the four-dimensional Pleban ́ski-Demian ́ski metric where they are proportional to the sum of the squares of the electric and the magnetic charges. As part of the derivation, we also find the two conformal Killing-Yano tensors of the Pleban ́ski-Demian ́ski metric in the recently introduced coordinates of Podolsky and Vratny. The construction of asymptotic charges for the Cotton current is elucidated and compared to the three-dimensional construction in Topologically Massive Gravity. For the three-dimensional case, we also give a conformal superspace multiplet that contains the Cotton current in the bosonic sector. In a mathematical section, we derive potentials for the currents, find identities for conformal KYTs and for KYTs in torsionful backgrounds.

Authors: Naser Ahmadiniaz, Filippo Maria Balli, Olindo Corradini, Cristhiam Lopez-Arcos, Alexander Quintero Vélez, Christian Schubert

Preprint number: UUITP-47/21

Abstract: The relation for the gravity polarisation as the tensor product of two gluon polarisation vectors has been well-known for a long time, but a version of this relation for multi-particle fields is still not present. Here we show that in order for this to happen we first have to ensure that the multi-particle polarisations satisfy colour-kinematics duality, which arises naturally from the Bern-Kosower formalism for one-loop gluon amplitudes, and later we will see that the tensor product for multi-particle fields arises naturally in the Bern- Dunbar-Shimada formalism for one-loop gravity amplitudes. This allows us to formulate a new prescription for double-copy gravity Berends-Giele currents that can be applied to other cases. To make this point we also present other examples. 

Authors: Markus Diehl, Jonathan R. Gaunt, Paolo Pichini and Peter Ploessl

Preprint number: UUITP-46/21

Abstract: We investigate the positivity of double parton distributions with a non-trivial dependence on the parton colour. It turns out that positivity is not preserved by leading-order evolution from lower to higher scales, in contrast to the case in which parton colour is summed over. We also study the positivity properties of the distributions at small distance between the two partons, where they can be computed in terms of perturbative splitting kernels and ordinary parton densities.

Authors: Vladimir Bashmakov, Nicola Gorini

Preprint number: UUITP-45/21

Abstract: We consider the IR phases of two-node quiver theories with N=1 supersymmetry in d=2+1 dimensions. It turns out that the discussion splits into two main cases, depending on whether the Chern-Simons levels associated with two nodes have the same sign, or the opposite signs, with the latter case being more non-trivial. The determination of the phase diagrams allows us to conjecture certain infrared dualities involving either two quiver theories, or a quiver and adjoint QCD. We also provide a short discussion of quivers possessing time reversal symmetry.

Authors: Simon Ekhammar, Dmytro Volin

Preprint number: UUITP-44/21

Abstract: We propose a procedure to derive quantum spectral curves of AdS/CFT type by requiring that a specially designed analytic continuation around the branch point results in an automorphism of the underlying algebraic structure. In this way we derive four new systems. Two are based on SU(2|2) symmetry, and we show that one of them describes Hubbard model. Two more are based on SU(2|2)xSU(2|2). In the special subcase of PSU(1,1|2)xPSU(1,1|2) we get the unique nontrivial option and hence it is a natural candidate for the quantum spectral curve for AdS3/CFT2 integrability for AdS3xS3xS3xT4 background supported by RR-flux.

Authors: Lara B. Anderson, James Gray, Mohsen Karkheiran, Paul-Konstantin
 Oehlmann and Nikhil Raghuram

Preprint number: UUITP-43/21

Abstract: In this work we study F-theory compactifications on elliptically fibered
Calabi-Yau n-folds which have $\mathbb{P}^1$-fibered base manifolds. Such
geometries, which we study in both 4- and 6-dimensions, are both ubiquitous
within the set of Calabi-Yau manifolds and play a crucial role in
heterotic/F-theory duality. We discuss the most general formulation of
$\mathbb{P}^1$-bundles of this type, as well as fibrations which degenerate at
higher codimension loci. In the course of this study, we find a number of new
phenomena. For example, in both 4- and 6-dimensions we find transitions whereby
the base of a $\mathbb{P}^1$-bundle can change nature, or "jump", at certain
loci in complex structure moduli space. We discuss the implications of this
jumping for the associated heterotic duals. We argue that
$\mathbb{P}^1$-bundles with only rational sections lead to heterotic duals
where the Calabi-Yau manifold is elliptically fibered over the section of the
$\mathbb{P}^1$- bundle, and not its base. As expected, we see that
degenerations of the $\mathbb{P}^1$-fibration of the F-theory base correspond
to 5-branes in the dual heterotic physics, with the exception of cases in which
the fiber degenerations exhibit monodromy. Along the way, we discuss a set of
useful formulae and tools for describing F-theory compactifications on this
class of Calabi-Yau manifolds.

Authors: Daniele Dorigoni, Axel Kleinschmidt and Oliver Schlotterer

Preprint number: UUITP-42/21

Abstract: We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincaré series in a companion paper. The source term of the Laplace equation is a product of (derivatives of) two non-holomorphic Eisenstein series whence the modular invariants are assigned depth two. These modular invariant functions can sometimes be expressed in terms of single-valued iterated integrals of holomorphic Eisenstein series as they appear in generating series of modular graph forms. We show that the set of iterated integrals of Eisenstein series has to be extended to include also iterated integrals of holomorphic cusp forms to find expressions for all modular invariant functions of depth two. The coefficients of these cusp forms are identified as ratios of their L-values inside and outside the critical strip.

Authors: Daniele Dorigoni, Axel Kleinschmidt and Oliver Schlotterer

Preprint number: UUITP-41/21

Abstract: We derive new Poincaré-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus one. The Poincaré series are constructed from iterated integrals over single holomorphic Eisenstein series and their complex conjugates, decorated by suitable combinations of zeta values. We evaluate the Poincaré sums over these iterated Eisenstein integrals of depth one and deduce new representations for all modular graph forms built from iterated Eisenstein integrals at depth two. In a companion paper, some of the Poincaré sums over depth-one integrals going beyond modular graph forms will be described in terms of iterated integrals over holomorphic cusp forms and their L-values.

Authors: Michele Del Zotto, Jihwan Oh, Yehao Zhou

Preprint number: UUITP-40/21

Abstract: In this short note, we present some evidence towards the existence of an algebra of BPS G₂ instantons. These are instantonic configurations that govern the partition functions of 7d SYM theories on local G₂ holonomy manifolds X. To shed light on such structure, we begin investigating the relation with parent 4d N=1 theories obtained by geometric engineering M-theory on X. The main point of this paper is to substantiate the following dream: the holomorphic sector of such theories on multi-centered Taub-NUT spaces gives rise to an algebra whose characters organise the G₂ instanton partition function. As a first step towards this program, we argue by string duality that a multitude of geometries X exist that are dual to well-known 4d SCFTs arising from D3 branes probes of CY cones: all these models are amenable to analysis along the lines suggested by Dijkgraaf, Gukov, Neitzke and Vafa in the context of topological M-theory. Moreover, we discuss an interesting relation to Costello's twisted M-theory, which arises at local patches, and is a key ingredient in identifying the relevant algebras.

Authors: Sergio Cecotti, Michele Del Zotto, Mario Martone, and Robert Moscrop

Preprint: UUITP-39/21

Abstract: In this paper we introduce the characteristic dimension of a four dimensional N=2 superconformal field theory, which is an extraordinary simple invariant determined by the scaling dimensions of its Coulomb branch operators. We prove that only nine values of the characteristic dimension are allowed, −∞, 1 ,6/5, 4/3, 3/2, 2, 3, 4, and 6, thus giving a new organizing principle to the vast landscape of 4d N=2 SCFTs. Whenever the characteristic dimension differs from 1 or 2, only very constrained special Kähler geometries (i.e. isotrivial, diagonal and rigid) are compatible with the corresponding set of Coulomb branch dimensions and extremely special, maximally strongly coupled, BPS spectra are allowed for the theories which realize them. Our discussion applies to superconformal field theories of arbitrary rank, i.e. with Coulomb branches of any complex dimension. Along the way, we predict the existence of new N=3 theories of rank two with non-trivial one-form symmetries.

Author: Max Guillen

Preprint number: UUITP-38/21

Abstract: Bosonic and RNS chiral strings have been defined from a singular gauge fixing of the respective Polyakov and spinning string actions, enforcing, among other things, the finite nature of their physical spectra. Except for the heterotic case, the tensionless limits of such chiral models have been shown to describe the same field theories predicted by their ambitwistor analogues. In this paper, we study the Green-Schwarz formulation for Type II and heterotic superstrings in a singular gauge. After performing a light-cone gauge analysis, their physical spectra are shown to match those of RNS chiral strings, and their respective tensionless limits are found to describe the same field theories predicted by RNS ambitwistor strings. Their pure spinor counterparts are then introduced by making use of the Oda-Tonin method. In doing so, symmetries hidden in the pure spinor ambitwistor string action become manifest, proposals motivating the sectorized pure spinor BRST charges find simple grounds, and integrated vertex operators emerge naturally.

Authors: Maor Ben-Shahar and Max Guillen

Preprint number: UUITP-37/21

Abstract: Using the pure spinor master action for 10D super-Yang-Mills in the gauge $b_{0}V = Q\Xi$, tree-level scattering amplitudes are calculated through the perturbiner method, and shown to match those obtained from pure spinor CFT techniques. We find kinematic numerators made of nested $b$-ghost operators, and show that the Siegel gauge condition $b_{0}V = 0$ gives rise to color-kinematics duality satisfying numerators whose Jacobi identity follows from that of a kinematic algebra.

Authors: Harold Erbin, Riccardo Finotello, Robin Schneider and Mohamed Tamaazousti

Preprint number: UUITP-36/21

Abstract: We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi-Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi-Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for $h^{(1,1)}$ and 97% for $h^{(2,1)}$ (100% for both), 81% (96%) for $h^{(3,1)}$, and 49% (83%) for $h^{(2,2)}$. Assuming that the Euler number is known (since it is easy to compute) and taking into account the linear constraint arising from index computations, we get 100% total accuracy.

Authors: Eric D'Hoker and Oliver Schlotterer

Preprint number: UUITP-35/21

Abstract: The contribution from even spin structures to the genus-two amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help of loop momenta this problem reduces to the evaluation of the corresponding chiral amplitude, which is carried out using the same techniques that were used for the genus-two amplitude with four external NS states. The results agree with the parity-even NS components of a construction using chiral splitting and pure spinors given in earlier companion papers arXiv:2006.05270 and arXiv:2008.08687.

Authors: Marco Chiodaroli, Henrik Johansson and Paolo Pichini

Preprint number: UUITP-34/21

Abstract: Quantum scattering amplitudes for massive matter have received new attention in connection to classical calculations relevant to gravitational-wave physics. Amplitude methods and insights are now employed for precision computations of observables needed for describing the gravitational dynamics of bound massive objects such as black holes. An important direction is the inclusion of spin effects needed to accurately describe rotating (Kerr) black holes. Higher-spin amplitudes introduced by Arkani-Hamed, Huang and Huang at three points have by now a firm connection to the effective description of Kerr black-hole physics. The corresponding Compton higher-spin amplitudes remain however an elusive open problem. Here we draw from results of the higher-spin literature and show that physical insights can be used to uniquely fix the Compton amplitudes up to spin 5/2, by imposing a constraint on a three-point higher-spin current that is a necessary condition for the existence of an underlying unitary theory. We give the unique effective Lagrangians up to spin 5/2, and show that they reproduce the previously-known amplitudes. For the multigraviton amplitudes analogous to the Compton amplitude, no further corrections to our Lagrangians are expected, and hence such amplitudes are uniquely predicted. As an essential tool, we introduce a modified version of the massive spinor-helicity formalism which allows us to conveniently obtain higher-spin states, propagators and compact expressions for the amplitudes

Authors: Agnese Bissi, Parijat Dey and Giulia Fardelli

Preprint number: UUITP-33/21

Abstract: We review the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are based solely on symmetries, in particular in the analytic structure and in the associativity of the operator product expansion. We focus on two applications of the analytic conformal bootstrap: the study of the $\epsilon$ expansion of the Wilson Fisher model via the introduction of a dispersion relation and the large $N$ expansion of maximally supersymmetric Super Yang Mills theory in four dimensions. 

Authors: Luca Cassia and Maxim Zabzine

Preprint number: UUITP-32/21

Abstract: We consider the matrix model of U(N) refined Chern-Simons theory on S³ for the unknot. We derive a q-difference operator whose insertion in the matrix integral reproduces an infinite set of Ward identities which we interpret as q-Virasoro constraints. The constraints are rewritten as difference equations for the generating function of Wilson loop expectation values which we solve as a recursion for the correlators of the model. The solution is repackaged in the form of superintegrability formulas for Macdonald polynomials. Additionally, we derive an equivalent q-difference operator for a similar refinement of ABJ theory and show that the corresponding q-Virasoro constraints are equal to those of refined Chern-Simons for a gauge super-group U(N|M). Our equations and solutions are manifestly symmetric under Langlands duality q ↔ 1/t which correctly reproduces 3d Seiberg duality when q is a specific root of unity.

Authors: Alex Edison, Max Guillen, Henrik Johansson, Oliver Schlotterer and Fei Teng

Preprint number: UUITP-31/21

Abstract: In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators D^{2k} F^n and D^{2k} R^n in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension alpha'. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-loop versions of the monodromy and KLT relations. We express a variety of four- and five-point examples in terms of quadratic propagators and formulate a criterion on the underlying genus-one correlation functions that should make this recombination possible at all orders in alpha'. The ultraviolet divergences of the one-loop matrix elements are crosschecked against the non-separating degeneration of genus-one integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.

Authors: Joseph Minahan, Usman Naseer and Charles Thull

Preprint number: UUITP-30/21

We consider mass-deformed theories with ${\cal N}\geq2$ supersymmetry on round and squashed three-spheres. By embedding the supersymmetric backgrounds in extended supergravity we show that at special values of mass deformations the supersymmetry is enhanced on the squashed spheres. When the $3d$ partition function can be obtained by a limit of a $4d$ index we also show that for these special mass deformations only the states annihilated by extra supercharges contribute to the index. By using an equivalence between partition functions on squashed spheres and ellipsoids,  we explain the recently observed squashing independence of the partition function of mass-deformed ABJM theory  on the  ellipsoid. We provide further examples of such simplification for various $3d$ supersymmetric theories.

Authors: N. Cribiori, D. Junghans, V. Van Hemelryck, T. Van Riet, T. Wrase

Preprint number: UUITP-29/21

Abstract: We revisit various aspects of AdS$_4$ flux vacua with scale separation in type II supergravity and M-theory. We show that massless IIA allows both weakly and strongly coupled solutions for which the classical orientifold backreaction can be tuned small. This is explicitly verified by computing the backreaction at leading order in perturbation theory. We give evidence that the strongly coupled solutions can be lifted to scale-separated and sourceless (but classically singular) geometries in 11D supergravity.

Authors: Andreas P. Braun, Paul-Konstantin Oehlmann, and Magdalena Larfors

Preprint number: UUITP-28/21

Abstract: We study six dimensional supergravity theories with superconformal sectors(SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally F-Theory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2-form global symmetries of the SCFT sectors. For both $(2,0)$ and $(1,0)$ theories we show that whenever the charge lattice of the SCFT sectors is non-primitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2-form symmetries that remains unbroken by BPS strings. By the absence of global symmetries in quantum gravity, this subgroup much be gauged. Using the embedding of the charge lattices also allows us to determine how the gauged 2-form symmetry embeds into the 2-form global symmetries of the SCFT sectors, and we present several concrete examples, as well as some general observations. As an alternative derivation, we recover our results for a large class of models from a dual perspective upon reduction to five dimensions.

Authors: Parijat Dey and Nirmalya Kajuri

Preprint number: UUITP-27/21

Abstract: In the bulk reconstruction program, one constructs boundary representations of bulk fields. However, the boundary representations derived in global and AdS-Rindler coordinates appear to be inequivalent as the AdS-Rindler smearing function is known to diverge in dimensions greater than two. This is an apparent paradox. We investigate the relation between the two representations for AdS$_2$. We obtain the AdS-Rindler smearing function for massive and massless fields and show that the global and AdS-Rindler boundary representations are related by conformal transformations. We also use the boundary representations of creation and annihilation operators to compute the Bogoliubov transformation relating global modes to AdS-Rindler modes for both massive and massless particles.

Authors: Miguel Montero, Cumrun Vafa, Thomas Van Riet and Gerben Venken

Preprint number: UUITP-26/21

Abstract: Demanding that charged Nariai black holes in (quasi-)de Sitter space decay
without becoming super-extremal implies a lower bound on the masses of charged particles, known as the Festina Lente (FL) bound. In this paper we elucidate various aspects of this bound as well as extensions of it to d > 4 and to situations with scalar potentials and dilatonic couplings. We also discuss phenomenological implications of FL including an explanation of why the Higgs potential cannot have a local minimum at the origin, thus explaining why the weak force must be broken. For constructions of meta-stable dS involving anti-brane uplift scenarios, even though the throat region is consistent with FL, the bound implies that we cannot have any light charged matter elds coming from any far away region in the compactified geometry, contrary to the fact that they are typically expected to arise in these scenarios. This strongly suggests that introduction of warped anti-branes in the throat cannot be decoupled from the bulk dynamics as is commonly assumed. Finally, we provide some evidence that in certain situations the FL bound can have implications even with gravity decoupled and illustrate this in the context of non-compact throats.

Authors: Luca Griguolo, Rodolfo Panerai, Jacopo Papalini, Domenico Seminara

Preprint number: UUITP-25/21

Abstract: We investigate the nonperturbative structure of Jackiw-Teitelboim gravity at finite cutoff, as given by its proposed formulation in terms of a TT-deformed Schwarzian quantum mechanics. Our starting point is a careful computation of the disk partition function to all orders in the perturbative expansion in the cutoff parameter. We show that the perturbative series is asymptotic and that it admits a precise completion exploiting the analytical properties of its Borel transform, as prescribed by resurgence theory. The final result is then naturally interpreted in terms of the nonperturbative branch of the TT-deformed spectrum. The finite-cutoff trumpet partition function is computed by applying the same strategy. In the second part of the paper, we propose an extension of this formalism to arbitrary topologies, using the basic gluing rules of the undeformed case. The Weil-Petersson integrations can be safely performed due to the nonperturbative corrections and give results that are compatible with the flow equation associated with the TT deformation. We derive exact expressions for general topologies and show that these are captured by a suitable deformation of the Eynard-Orantin topological recursion. Finally, we study the "slope" and "ramp" regimes of the spectral form factor as functions of the cutoff parameter.

Authors: S. Ekhammar, B. E. W. Nilsson

Preprint number: UUITP-24/21

Abstract: We derive major parts of the eigenvalue spectrum of the operators on the squashed seven-sphere that appear in the compactification of eleven-dimensional supergravity. These spectra determine the mass spectrum of the fields in AdS₄ and are important for the corresponding N =1 supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in AdS₄ was derived for this compactification. Some comments are also made concerning the G₂ holonomy and its implications on the structure of the operator equations on the squashed seven-sphere.

Authors: U. H. Danielsson, D. Panizo, R. Tielemans, T. Van Riet

Preprint number: UUITP-22/21

Abstract: We argue that the choice of boundary condition for the wavefunction in quantum cosmology depends on the UV completion of general relativity. We provide an explicit example using a braneworld scenario in which a de Sitter cosmology is induced on the surface of a CDL bubble in a 5-dimensional AdS space. The corresponding boundary conditions are unambigously fixed by demanding consistency with the known physics of bubble nucleation and this selects the Vilenkin choice from a 4D viewpoint.

Authors: Gang Chen, Henrik Johansson, Fei Teng and Tianheng Wang

Preprint number: UUITP-21/21

Abstract: Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding open problem that only has had partial success for simple helicity sectors. In past work, we introduced a framework using tensor currents and fusion rules to generate BCJ numerators of a special subsector of NMHV amplitudes in Yang-Mills theory. Here we enlarge the scope and explicitly realize a kinematic algebra for all NMHV amplitudes. Master numerators are obtained directly from the algebraic rules and through commutators and kinematic Jacobi identities other numerators can be generated. Inspecting the output of the algebra, we conjecture a closed-form expression for the master BCJ numerator up to any multiplicity. We also introduce a new method, based on group algebra of the permutation group, to solve for the generalized gauge freedom of BCJ numerators. It uses the recently introduced binary BCJ relations to provide a complete set of NMHV kinematic numerators that consist of pure gauge.

Authors: Ulf Lindström and Özgür Sarioglu

Preprint number: UUITP-20/21

Authors: Simon Ekhammar, Dmytro Volin

Preprint number: UUITP-19/21

Abstract: We propose a gl(r)-covariant parameterisation of Bethe algebra appearing in so(2r) integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials.

Authors: Paolo di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano

Preprint number: UUITP-18/21

Abstract: Using N=8 supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its non-relativistic (NR) and ultra-relativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential sub-region. This task is efficiently carried out by using the method of differential equations with complete near-static boundary conditions. In contrast to the potential-region result, the physical deflection angle includes radiation-reaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energy-momentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic tree-level amplitude, we are able to treat N=8 and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein's gravity by the addition of the radiation-reaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.

Authors: Max Guillen, Henrik Johansson, Renann Lipinski Jusinskas, Oliver Schlotterer

Preprint number: UUITP-17/21

Abstract: We present a new method, exact in alpha', to explicitly compute string tree-level amplitudes involving one massive state and any number of massless ones. This construction relies on the so-called twisted heterotic string, which admits only gauge multiplets, a gravitational multiplet, and a single massive supermultiplet in its spectrum. In this simplified model, we determine the moduli-space integrand of all amplitudes with one massive state using Berends-Giele currents of the gauge multiplet. These integrands are then straightforwardly mapped to gravitational amplitudes in the twisted heterotic string and to the corresponding massive amplitudes of the conventional type-I and type-II superstrings.