Supersymmetric Rényi entropy and Anomalies in 6d (1,0) SCFTs

A closed formula of the universal part of supersymmetric Rényi 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 ν = 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 Rényi entropy to an equivariant integral of the anomaly polynomial in even dimensions and check it against known data in 4d and 6d.