Short interval expansion of R\'enyi entropy on torus

TL;DR

This paper develops a method to compute the short interval expansion of R'enyi entropy in 2D CFTs on a torus, matching holographic results and including effects of chemical potential.

Contribution

It provides a systematic short interval expansion of R'enyi entropy for 2D CFTs on a torus, including large central charge and chemical potential effects, with holographic comparisons.

Findings

Agreement with holographic results at order ^6

Read off 1/c contributions from the expansion

Extended analysis to include chemical potential

Abstract

We investigate the short interval expansion of the R\'enyi entropy for two-dimensional conformal field theory (CFT) on a torus. We require the length of the interval $\ell$ to be small with respect to the spatial and temporal sizes of the torus. The operator product expansion of the twist operators allows us to compute the short interval expansion of the R\'enyi entropy at any temperature. In particular, we pay special attention to the large $c$ CFTs dual to the AdS$_3$ gravity and its cousins. At both low and high temperature limits, we read the R\'enyi entropies to order $\ell^6$, and find good agreements with holographic results. Moreover, the expansion allows us to read $1/c$ contribution, which is hard to get by expanding the thermal density matrix. We generalize the study to the case with the chemical potential as well.