Supersymmetric Renyi Entropy and Weyl Anomalies in Six-Dimensional (2,0) Theories

TL;DR

This paper derives a universal formula for supersymmetric R'enyi entropy in six-dimensional (2,0) theories, linking it to Weyl anomalies and providing insights into anomaly bounds and free energy on squashed spheres.

Contribution

It presents a closed-form expression for supersymmetric R'enyi entropy in 6D (2,0) theories, connecting it to Weyl anomalies and deriving it through multiple methods.

Findings

R'enyi entropy is a cubic polynomial in 1/q with coefficients related to Weyl anomalies.

The formula is consistent with free tensor multiplet results and anomaly coefficient assumptions.

A possible lower bound on the ratio of Weyl anomalies is suggested.

Abstract

We propose a closed formula of the universal part of supersymmetric R\'enyi entropy $S_q$ for $(2,0)$ superconformal theories in six-dimensions. We show that $S_q$ across a spherical entangling surface is a cubic polynomial of $\gamma:=1/q$, with all coefficients expressed in terms of the newly discovered Weyl anomalies $a$ and $c$. This is equivalent to a similar statement of the supersymmetric free energy on conic (or squashed) six-sphere. We first obtain the closed formula by promoting the free tensor multiplet result and then provide an independent derivation by assuming that $S_q$ can be written as a linear combination of 't Hooft anomaly coefficients. We discuss a possible lower bound ${a\over c}\geq {3\over 7}$ implied by our result.