# $3d$ One-form Mixed Anomaly and Entanglement Entropy

## TL;DR

This paper investigates the mixed anomaly between two one-form symmetries in 3D Chern-Simons theories by analyzing the entanglement entropy of linked symmetry lines, revealing a new measure of the anomaly.

## Contribution

It introduces a novel approach to quantify mixed anomalies using entanglement entropy of linked Wilson loops in 3D gauge theories.

## Key findings

- Entanglement entropy captures the mixed anomaly between symmetry groups.
- The difference in entanglement entropy measures the anomaly.
- Linked Wilson loops encode the topological features related to anomalies.

## Abstract

We study mixed anomaly between $G_1$ and $G_2$ of one-form finite symmetry $G_1\times G_2$ in $3d$ Chern-Simons theories. We assign a quantum entanglement structure to two linked $G$-symmetry lines (Wilson loops) and compute the entanglement entropy $S[G]$. We find a measure of the mixed anomaly by computing $S[G_1\times G_2]-S[G_1]-S[G_2]$.