Exploring Symmetry Categories of Quantum Fields

Quantum field theory (QFT) is a universal language for modern theoretical physics, with a wide variety of applications ranging from condensed matter, particle physics and cosmology.

Despite its striking success in all these areas, we still lack tools to completely characterize the full phase diagram of quantum fields, mostly due to non-perturbative effects. In QFT the dynamics of physical systems is described exploiting correlators. Most of the tools developed so far have focused on studying the correlators among point-like fluctuations of the field.

It is well-known however that the quantum field can have also extended fluctuations, organized for instance along lines instead of points.

Constraints for the correlators among the point-like and the extended fluctuations are encoded by a new type of symmetries, called higher symmetries and organized by symmetry categories.Symmetry categories give a language to capture the conservation laws for extended field configurations. In this project we study how patterns of breaking of symmetry categories are related to the phase diagrams of QFTs.

In the first part of the project we will develop tools to compute symmetry categories indepedent from a conventional Lagrangian perturbative descritpion. In the second part of the project we will appy these tools to non-perturbative QFTs.

It is important to develop these techniques towards a more comprehensive understanding of the phases of QFTs with many interdisciplinary implications.