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

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 $S[G_1\times G_2]-S[G_1]-S[G_2]$.

arXiv comment27+1 pages

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• Fermionization of conformal boundary states
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• $Z_3$ and $(\times Z_3{)}^3$ symmetry protected topological paramagnets
• Multi-boundary entanglement in Chern-Simons theory with finite gauge groups
• Topological entanglement and hyperbolic volume
• Topological entanglement and number theory
• Large-party limit of topological entanglement entropy in Chern-Simons theory