Holographic R\'enyi entropy for two-dimensional $\mathcal{N}$=(2,2) superconformal field theory

Understand

We investigate the holographic R\'enyi entropy for two-dimensional $\mathcal N=(2,2)$ superconformal field theory (SCFT), which is dual to $\mathcal N=2$ supergravity in AdS$_3$ background.

• In SCFT we have the stress tensor, current, and their supersymmetric partners, and in supergravity we have the graviton, vector field, and two gravitinos.
• We get the R\'enyi mutual information of two short intervals on complex plane in expansion by the cross ratio $x$ to order $x^4$, and R\'enyi entropy of one interval on 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 in both the supergravity and SCFT sides, and find matches of the results.