The Memory of Solitons

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.