# The Memory of Solitons

ERC starting grant #851931

## Details

- Period: 2020-02-01 – 2025-01-31
- Budget: 17,418,000 SEK
- Funder: EU – Horizon Europe – ERC

## Description

Quantum field theory (QFT) is undoubtedly one of the most important achievements of modern theoretical physics, with broad applications ranging from condensed matter systems to elementary particle physics. Despite its successes, the current formulation of QFT is incomplete and we lack tools to address from first principles a wide variety of interesting physical systems, including the dynamics of quarks within protons, phase transitions, and high temperature superconductors.

The present project aims at addressing this issue by establishing a novel, powerful and unconventional paradigm for QFT without relying upon the existence of a perturbative expansion.

The cornerstone for such a paradigm is the following remark: in a wide variety of simple examples it is possible to compute exactly the values of several observables relying solely upon the knowledge of the spectrum of solitons of the given QFT: this effect is *the memory of solitons*. The main purpose of this project is to develop and exploit the memory of solitons to study non-perturbative aspects of QFTs.

Our strategy to approach this problem is twofold. On the one hand we focus on the simplest QFTs to develop intuition on concrete and explicit examples: our theoretical laboratory consists of theories having supersymmetry and/or conformal symmetry where a plethora of exact results are available. On the other, we exploit geometric engineering techniques in string theory, which gives access to the non-perturbative spectrum of QFTs from a completely different angle that allows exact computations to be performed, providing new insights into the mathematical structure of the theories involved.

The geometric engineering techniques we adopt are intertwined with the geometric structures of special holonomy manifolds and their enumerative invariants. These are tools to determine the solitonic spectrum in terms of geometric data for the models in our theoretical laboratory.

Among the first results of the project we have determined the global strucutres and higher form symmetries of a wide variety of SCFTs in 4,5 and 6 dimensions, with and without a conventional Lagrangian formulation.

## Project members

## Project Affiliates

Shani Nadir Meynet (Postdoc - Mathematics Department)

Kaiwen Sun (Postdoc - Theoretical physics group)

Daniele Migliorati (PhD student - Mathematics Department)

## Former members

Postdocs: Vladimir Bashmakov, Muyang Liu, Paul-Konstantin Öhlmann

## Activities

We will publish below activities related to this project

- Nordita Program: Categorical Aspects of Symmetries (August 14-25, 2023)
- UU Workshop: Engineering in the Landscape: Geometry, Symmetries, and Anomalies (August 24-26, 2022)
- Mittag-Leffler Workshop: Enumerative Invariants, Quantum Fields and String Theory Correspondences (July 25-29, 2022)

Since February 2020, we are co-organizing the joint string-math seminar at Uppsala University.

## Publications and Preprints

- The ALE Partition Functions of M-String Orbifolds, MDZ, Guglielmo Lockhart, e-Print: 2311.08462
- 5d Conformal Matter, MDZ, Mario De Marco, Michele Graffeo, Andrea Sangiovanni, e-Print: 2311.04984
- Topological defects, Nils Carqueville, MDZ, Ingo Runkel, e-Print: 2311.02449
- The ALE Partition Functions of M-Strings, MDZ, Guglielmo Lockhart, e-Print: 2309.00607
- The Higgs branch of Heterotic ALE instantons, MDZ, Marco Fazzi, Suvendu Giri, e-Print: 2307.11087
- A new vista on the Heterotic Moduli Space from Six and Three Dimensions, MDZ, Marco Fazzi, Suvendu Giri, e-Print: 2307.10356
- Higher Structure of Chiral Symmetry, Christian Copetti, MDZ, Kantaro Ohmori, Yifan Wang, e-Print: 2305.18282
- Four-manifolds and Symmetry Categories of 2d CFTs, Vladimir Bashmakov, MDZ, Azeem Hasan, e-Print: 2305.10422
- Junctions, Edge Modes, and G2G2-Holonomy Orbifolds, Bobby Acharya, MDZ, Jonathan J. Heckman, Max Hubner, Ethan Torres, e-Print: 2304.03300
- 6D Heterotic Little String Theories and F-theory Geometry: An Introduction, MDZ, Muyang Liu, Paul-Konstantin Oehlmann, e-Print: 2303.13502
- Back to Heterotic Strings on ALE Spaces: Part II -- Geometry of T-dual Little Strings, MDZ, Muyang Liu, Paul-Konstantin Oehlmann, e-Print: 2212.05311
- Non-invertible symmetries of class S theories, Vladimir Bashmakov, MDZ, Azeem Hasan, Justin Kaidi, e-Print: 2211.05138
- Back to heterotic strings on ALE spaces. Part I. Instantons, 2-groups and T-duality, MDZ, Muyang Liu, Paul-Konstantin Oehlmann, e-Print: 2209.10551
- On the 6d Origin of Non-invertible Symmetries in 4d, Vladimir Bashmakov, MDZ, Azeem Hasan, e-Print: 2206.07073
- Global Structures from the Infrared, MDZ and Iñaki García Etxebarria (Durham), e-Print: 2204.06495
- 2-Group Symmetries and M-Theory, MDZ, Iñaki García Etxebarria (Durham), and Sakura Shäfer-Nameki (Oxford U), e-Print: 2203.10097
- Higher Symmetries of 5d Orbifold SCFTs, MDZ, Jonathan J. Heckman (Penn U), Shani Nadir Meynet (Uppsala U and SISSA), Robert Moscrop (Uppsala U), Hao Y. Zhang (Penn U), e-Print: 2201.08372
- F-theory on 6D Symmetric Toroidal Orbifolds, Finn Bjarne Kohl (Munster U), Magdalena Larfors (Uppsala U), Paul-Konstantin Öhlmann, e-Print: 2111.07998
- Phases of N=1 Quivers in 2+1 Dimensions, Vladimir Bashmakov, Nicola Gorini (Bicocca U), e-Print: 2109.11862
- Evidence for an Algebra of
*G2* Instantons, MDZ, Jihwan Oh (Oxford U), Yehao Zhou (PI), e-Print: 2109.01110 - The Characteristic Dimension of Four-dimensional N=2 SCFTs, Sergio Cecotti (SISSA), MDZ, Mario Martone (SCGP), Robert Moscrop, e-Print: 2108.10884
- Maruyoshi-Song flows and defect groups of Dbp(G) theories, Saghar Hosseini (Durham U), Robert Moscrop, Published in:
*JHEP***2021**119, e-Print: 2106.03878 - Playing with the index of M-theory, MDZ, Nikita Nekrasov (SCGP), Nicolò Piazzalunga (Uppsala U), and Maxim Zabzine (Uppsala U), e-Print: 2103.10271
- 2-Group Symmetries of 6d Little String Theories and T-duality, MDZ, and Kantaro Ohmori (IAS and SCGP), Published in:
*Annales Henri Poincaré*(2021), e-Print: 2009.03489 - Higher form symmetries of Argyres-Douglas theories, MDZ, Iñaki García Etxebarria (Durham), and Saghar Hosseini (Durham), Published in:
*JHEP*10 (2020) 056, e-Print: 2007.15603 - Higher Form Symmetries and M-theory, Federica Albertini (Durham), MDZ, Iñaki García Etxebarria (Durham), and Saghar Hosseini (Durham), e-Print: 2005.12831 (accepted - to appear on JHEP)