Supersymmetric Renyi Entropy and Anomalies in Six-Dimensional (1,0) Superconformal Theories

Abstract

A closed formula of the universal part of supersymmetric R\'enyi entropy $S_q$ for six-dimensional $(1,0)$ superconformal theories is proposed. Within our arguments, $S_q$ across a spherical entangling surface is a cubic polynomial of $\nu=1/q$, with $4$ coefficients expressed as linear combinations of the 't Hooft anomaly coefficients for the $R$-symmetry and gravitational anomalies. As an application, we establish linear relations between the $c$-type Weyl anomalies and the 't Hooft anomaly coefficients. We make a conjecture relating the supersymmetric R\'enyi entropy to an equivariant integral of the anomaly polynomial in even dimensions and check it against known data in four dimensions and six dimensions.