Simons Lectures on Categorical Symmetries

TL;DR

This volume introduces the concept of global categorical symmetries in quantum field theories, providing foundational lectures and methods for newcomers to explore this powerful analytical tool.

Contribution

It compiles and presents foundational lecture notes on global categorical symmetries in QFT, emphasizing accessible explanations and methods for beginners.

Findings

Introduces symmetry categories and their applications in QFT

Explains the cobordism hypothesis in the context of symmetries

Provides a beginner-friendly overview of anomalies and finite symmetries

Abstract

Global Categorical Symmetries are a powerful new tool for analyzing quantum field theories. This volume compiles lecture notes from the 2022 and 2023 summer schools on Global Categorical Symmetries, held at the Perimeter Institute for Theoretical Physics and at the Swiss Map Research Station in Les Diableret. Specifically, this volume collects the lectures: * An introduction to symmetries in quantum field theory, Kantaro Ohmori * Introduction to anomalies in quantum field theory, Clay C\'ordova * Symmetry Categories 101, Michele Del Zotto * Applied Cobordism Hypothesis, David Jordan * Finite symmetry in QFT, Daniel S. Freed These volumes are devoted to interested newcomers: we only assume (basic) knowledge of quantum field theory (QFT) and some relevant maths. We try to give appropriate references for non-standard materials that are not covered. Our aim in this first volume is to illustrate some of the main questions and ideas together with some of the methods and the techniques necessary to begin exploring global categorical symmetries of QFTs.