We investigate the holographic Rényi entropy for two-dimensional $\mathcal{N}=(2,2)$ superconformal field theory (SCFT), which is dual to $\mathcal{N}=2$ supergravity in an ${\mathrm{AdS}}_3$ background. In SCFT we have the stress tensor, the current, and their supersymmetric partners, and in supergravity we have the graviton, the vector field, and two gravitinos. We get the Rényi mutual information of two short intervals on the complex plane in expansion by the cross ratio $x$ to order $x^4$, and the Rényi entropy of one interval on a torus in expansion by $q=\exp (-2\pi \beta /L)$, with $\beta$ being the inverse temperature and $L$ being the spatial period, to order $q^2$. We calculate on both the supergravity and SCFT sides, and we find matches of the results.

• Received 25 December 2016

DOI:https://doi.org/10.1103/PhysRevD.95.126009