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

TL;DR

This white paper surveys generalized symmetries in quantum field theory, extending beyond ordinary 0-form symmetries to higher-form, higher-group, non-invertible, and subsystem symmetries. It explains how anomaly concepts, particularly ’t Hooft anomaly matching and anomaly inflow via anomaly theories ${\cal A}_{d+1}$, constrain RG flows and IR dynamics across diverse theories, including Chern-Simons-matter systems and fracton models. The authors highlight how these generalized symmetries yield new phases, dualities, and dynamical constraints, with implications spanning high-energy theory, condensed matter, and quantum gravity. Overall, the work emphasizes the unifying role of generalized symmetries and their anomalies in shaping the landscape of quantum field theories.

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.