Thermal Bekenstein-Hawking entropy from the worldsheet

TL;DR

This paper calculates the leading contribution to the BTZ black hole entropy in bosonic string theory using worldsheet techniques, involving winding operators and a replica trick, providing a novel string-theoretic derivation of black hole entropy.

Contribution

It introduces a method to compute black hole entropy from worldsheet correlation functions using winding condensates and a replica trick in bosonic string theory.

Findings

Entropy expressed as a one-point function of a non-local operator.

Exact integration over the radial mode simplifies the problem.

Formulation of a precise replica trick using winding condensates.

Abstract

We define and compute the leading sphere diagram contribution to the entropy of the BTZ black hole supported by Kalb-Ramond flux in bosonic string theory. In a winding condensate description, integrating exactly over the constant mode for the radial direction of AdS$_3$ reduces the problem to one of the correlation functions of winding operators in the free theory. The volume of the residual PSL(2,$\mathbb{C}$) gauge group of the sphere is canceled by the action of conformal transformations on the winding interaction insertions. We formulate a precise version of the replica trick in terms of (infinitesimally) non-integer winding condensates to produce the entropy of the BTZ black hole. The resulting entropy can be calculated from the one-point function of a non-local operator on the worldsheet.