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

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 $\gamma :=1\mathrm{/}q$, 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.