# Symmetries and anomalies in quantum field theory: a modern perspective

Starting 27th October 2022 – every Thursday from 10-12am in B1 – ending 15th December 2022

In the first part of the course I will review standard perturbative anomalies (anomalous Word identities and anomaly polynomials) from gauge anomalies and their cancelation conditions, including the Green-Schwarz mechanism, to ABJ/Chiral anomalies. I will then describe non-perturbative anomalies, and when they can be canceled.

In the second part of the course I will introduce the modern topological definition of symmetries in quantum field theory, and their ’t Hooft anomalies and mixed ’t Hooft anomalies. In particular, I will focus on the concept of symmetry and anomaly theory, and how it is useful to encode ’t Hooft Anomalies for discrete and higher-form symmetries. I will finally discuss the dynamical consequences of these ’t Hooft anomalies and the consequences of gauging a symmetry involved in a mixed anomaly, and various properties of the resulting QFT after this operation.

**Learning results of the course:**

The students will learn the modern definition of symmetry, which involves various generalisations that are useful for particle physics and condensed matter systems. They will then learn the basic tools to compute anomalies for these symmetries, including various modern topological techniques following from the definition of symmetry and anomaly theory. The student will also learn how anomalies can be used to constrain the strongly coupled non-perturbative physics of different systems, as well as various interesting consequences for the quantum field theory obtained by gauging a symmetry involved in a mixed ’t Hooft anomaly.

**Lecturer:**

Fabio Apruzzi