Line Defect Quantum Numbers & Anomalies

TL;DR

This paper investigates how line defects in gauge theories exhibit fractional quantum numbers related to 't Hooft anomalies, using Maxwell theory as a key example to analyze anomalies in non-Abelian gauge theories with matter.

Contribution

It establishes a detailed connection between symmetry fractionalization of line defects and 't Hooft anomalies, extending the understanding to non-Abelian gauge theories with matter fields.

Findings

Identifies symmetry fractionalization as a signal of 't Hooft anomalies.

Derives anomalies in $SU(2)$ gauge theories with various matter representations.

Shows the relation between line defect quantum numbers and known perturbative anomalies.

Abstract

We explore the connection between the global symmetry quantum numbers of line defects and 't Hooft anomalies. Relative to local (point) operators, line defects may transform projectively under both internal and spacetime symmetries. This phenomenon is known as symmetry fractionalization, and in general it signals the presence of certain discrete 't Hooft anomalies. We describe this in detail in the context of free Maxwell theory in four dimensions. This understanding allows us to deduce the 't Hooft anomalies of non-Abelian gauge theories with renormalization group flows into Maxwell theory by analyzing the fractional quantum numbers of dynamical magnetic monopoles. We illustrate this method in $SU(2)$ gauge theories with matter fermions in diverse representations of the gauge group. For adjoint matter, we uncover a mixed anomaly involving the 0-form and 1-form symmetries, extending previous results. For $SU(2)$ QCD with fundamental fermions, the 't Hooft anomaly for the 0-form symmetries that is encoded by the fractionalization patterns of lines in the Maxwell phase is a consequence of the familiar perturbative (triangle) anomaly.