Holographic R\'enyi Entropy of Single Interval on Torus: with W symmetry

TL;DR

This paper investigates the holographic R'enyi entropy of a single interval on a torus within CFTs possessing W symmetry, incorporating quantum corrections and confirming bulk-boundary consistency.

Contribution

It extends previous studies by including W symmetry effects and quantum corrections in the holographic R'enyi entropy calculation for a torus topology.

Findings

Computed thermal corrections up to order e^{-8π/TL} in CFT with W symmetry.

Calculated 1-loop quantum corrections in the gravity dual matching boundary results.

Achieved complete agreement between bulk and boundary computations.

Abstract

In this paper, we extend our study of the holographic R\'enyi entropy of single interval on a torus to the CFT with W symmetry. To read the possible corrections from W fields clearly, we compute the thermal correction to the R\'enyi entropy up to the order $e^{-8\pi /TL}$. In the field theory, this requires us to compute the contribution from all the level 4 states, from both the vacuum module and W primaries. On the gravity side, after computing the eigenvalue of single Schottky generators to the order $e^{-4 \pi/TL}$, we obtain the 1-loop quantum correction to the holographic R\'enyi entropy. We find complete agreement between the bulk and boundary theories.