Aspects of Entanglement Entropy in $3d$ $\mathcal{N}=2$ SCFTs

TL;DR

This paper explores entanglement entropy in 3d $ =2$ SCFTs, confirming its topological dependence and computing it at arbitrary coupling, revealing divergences linked to internal symmetries and universal contributions from multiplets.

Contribution

It provides the first computation of entanglement entropy at arbitrary coupling in 3d $ =2$ SCFTs, highlighting divergence origins and universal contributions from multiplets.

Findings

Supersymmetric entanglement entropy depends only on topology.

Divergences in entropy relate to charge fluctuations and internal symmetries.

Universal contributions from chiral and vector multiplets are identified.

Abstract

We investigate entanglement entropy in $3d$ $\mathcal{N}=2$ superconformal field theories from two different perspectives. We first confirm that the dependence of supersymmetric entanglement entropy (as defined in arXiv:1306.2958) on the entangling region is purely topological. We then compute entanglement entropy of $3d$ $\mathcal{N}=2$ superconformal gauge theories at arbitrary Yang-Mills coupling using the heat kernel method. This reveals a particular divergence originating in charge fluctuations in the vacuum, hence carrying information about internal symmetries of the theory. This computation leads to universal contributions to entanglement entropy from chiral and vector multiplets for unitary gauge groups of arbitrary rank, and has the advantage that the integral over the gauge moduli is simple to compute.