Stretched horizon, replica trick and off-shell winding condensate, and all that

TL;DR

This paper calculates stringy corrections to Schwarzschild black hole thermodynamics in large dimensions using worldsheet theory, confirming the Callan-Myers-Perry formula at leading and first correction order.

Contribution

It introduces an off-shell worldsheet formalism to compute exact $oldsymbol{ extit{ extalpha'}}$ corrections to black hole entropy, extending previous approaches.

Findings

Exact $oldsymbol{ extit{ extalpha'}}$ correction to black hole entropy obtained.

Leading order and first stringy correction match the Callan-Myers-Perry formula.

Thermodynamics at leading order insensitive to timelike Liouville details.

Abstract

$\alpha'$ corrections to near-horizon dynamics of a Schwarzschild black hole in a large number of spacetime dimensions $D$ are governed by the worldsheet theory composed of the cigar CFT and the classical sigma model on the sphere at the horizon, along with a timelike-Liouville theory of central charge $26-D$. At leading order in weak string coupling, blackhole thermodynamics is insensitive to the details of timelike Liouville theory. In this limit, we use Lewkowycz-Maldacena-trick motivated infinitesimally off-shell closed string worldsheet formalism in [arxiv: 2310.02313] to calculate thermal entropy exactly in $\alpha'$. The leading term in $\alpha'\to 0$ limit and the first stringy correction of our result are in precise agreement with the target space Callan-Myers-Perry formula.