Linking Entanglement and Discrete Anomaly

TL;DR

This paper explores the connection between entanglement and discrete anomalies in 3d Chern-Simons theories, proposing a new method to detect anomalies via Hopf state entanglement and validating it across various gauge groups.

Contribution

It introduces a systematic approach to identify discrete one-form anomalies using entanglement measures derived from the modular S matrix in 3d gauge theories.

Findings

Proposes a new entanglement-based detection method for discrete anomalies.

Validates the method across multiple gauge groups including A, B, C, D types.

Establishes a link between Hopf state entanglement and 't Hooft anomalies.

Abstract

In $3d$ Chern-Simons theory, there is a discrete one-form symmetry, whose symmetry group is isomorphic to the center of the gauge group. We study the 't Hooft anomaly associated to this discrete one-form symmetry in theories with generic gauge groups, $A,B,C,D$-types. We propose to detect the discrete anomaly by computing the Hopf state entanglement in the subspace spanned by the symmetry generators and develop a systematical way based on the truncated modular S matrix. We check our proposal for many examples.