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

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.