Generalized Global Symmetries

TL;DR

This paper introduces and explores generalized global symmetries characterized by charged operators of higher-dimensional operators, revealing their properties, anomalies, and implications for quantum field theories and topological phases.

Contribution

It provides a unified framework for understanding higher-form symmetries, their anomalies, and their role in various physical phenomena, extending the concept of ordinary global symmetries.

Findings

Generalized global symmetries include higher-dimensional charged operators.

They exhibit Ward identities and selection rules similar to ordinary symmetries.

The paper uncovers new insights into anomalies and symmetry breaking in quantum field theories.

Abstract

A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.