Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

TL;DR

This paper reviews recent advances in generalized symmetries in quantum field theory, highlighting their role in constraining dynamics and enabling new types of anomalies, with broad applications across the field.

Contribution

It provides a comprehensive overview of the latest developments in generalized symmetries, including categorical symmetries and their implications in quantum field theory.

Findings

Generalized symmetries include defect and subsystem symmetries.

New anomalies associated with these symmetries impose novel constraints.

Applications span various areas of quantum field theory and beyond.

Abstract

Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow for new kinds of anomalies that constrain dynamics. We review some transformative instances of these novel aspects of symmetry in quantum field theory, and give a broad-brush overview of recent applications.