Generalised Symmetries in Quantum Field Theories

During my DPhil I have explored generalised symmetries in quantum field theory, and more recently in lattice models. These represent a great advance towards the generalisation of the concept of symmetry, and have recently gained a lot of attention. In particular, I focused on the so-called categorical symmetries, which constitute a unifying concept of common interest across multiple fields such as high-energy and condensed matter physics, as well as having a strong connection with mathematics.

Symmetries play a central role in modern theoretical physics. They allow us to gain control over complex physical systems by revealing conserved quantities and providing tools to access the non-perturbative regime of theories. Not only they are very powerful in constraining the infra-red dynamics, they are also a fundamental guiding principle to organise phases of matter and predict novel states. It is therefore of great importance to uncover new kinds of symmetries and explore their dynamical implications.

Concretely, I have:

1. Uncovered new constructions of categorical symmetries in space-time dimensions higher than two.
2. Explored constraints of categorical symmetries on the phases of two dimensional theories, developing a categorical version of the well-established Landau paradigm of symmetry breaking.

The methodology is founded in mathematical physics, with a very strong component in algebraic topology and category theory.

This aligns with the EPSRC research strategy for mathematical physics, topology and condensed matter physics. This project stands out as an interdisciplinary research program, which connects to the vibrant research environment in the UK in said subjects.