Supersymmetric Rényi entropy and Weyl anomalies in six-dimensional (2,0) theories

Abstract

We propose a closed formula of the universal part of supersymmetric Rényi 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 γ := 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 $$ \frac{a}{c}\ge \frac{3}{7} $$ implied by our result.