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

Abstract

${\alpha }^{\prime }$ 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 ${\alpha }^{\prime }$. The leading term in ${\alpha }^{\prime }\to 0$ limit and the first stringy correction of our result are in precise agreement with the target space Callan-Myers-Perry formula.

29 pages, 2 figures