Perturbative String Thermodynamics near Black Hole Horizons

TL;DR

This paper investigates string thermodynamics near black hole horizons, emphasizing long strings' role, analyzing the thermal scalar, and discussing the breakdown of perturbation theory in black hole spacetimes.

Contribution

It advances understanding of near-Hagedorn string thermodynamics, provides new computations for cigar orbifold partition functions, and explores the breakdown of string perturbation theory in black hole backgrounds.

Findings

Long strings are crucial for black hole thermodynamics.

No $ extalpha'$-corrections for the heterotic thermal scalar in Rindler space.

Perturbation theory breaks down at high genus in black hole spacetimes.

Abstract

We provide further computations and ideas to the problem of near-Hagedorn string thermodynamics near (uncharged) black hole horizons, building upon our earlier work JHEP 1403 (2014) 086. The relevance of long strings to one-loop black hole thermodynamics is emphasized. We then provide an argument in favor of the absence of $\alpha'$-corrections for the (quadratic) heterotic thermal scalar action in Rindler space. We also compute the large $k$ limit of the cigar orbifold partition functions (for both bosonic and type II superstrings) which allows a better comparison between the flat cones and the cigar cones. A discussion is made on the general McClain-Roth-O'Brien-Tan theorem and on the fact that different torus embeddings lead to different aspects of string thermodynamics. The black hole/string correspondence principle for the 2d black hole is discussed in terms of the thermal scalar. Finally, we present an argument to deal with arbitrary higher genus partition functions, suggesting the breakdown of string perturbation theory (in $g_s$) to compute thermodynamical quantities in black hole spacetimes.