On Small Black Holes in String Theory

TL;DR

This paper explores the behavior of small black holes in string theory near the Hagedorn temperature, revealing enhanced symmetries and connections to two-dimensional models, with implications for D-brane systems and black hole thermodynamics.

Contribution

It introduces a modified effective theory for black holes near the Hagedorn temperature, extending analysis to higher dimensions and connecting black hole physics with non-abelian models and D-brane systems.

Findings

Enhanced SU(2) symmetry at the Hagedorn temperature

Connection between Schwarzschild black holes and 2D black holes at large dimensions

Identification of a Kondo-type model in D-brane systems

Abstract

We discuss the worldsheet sigma-model whose target space is the $d+1$ dimensional Euclidean Schwarzschild black hole. We argue that in the limit where the Hawking temperature of the black hole, $T$, approaches the Hagedorn temperature, $T_H$, it can be described in terms of a generalized version of the Horowitz-Polchinski effective theory. For $d\geq6$, where the Horowitz-Polchinski EFT [1,2] does not have suitable solutions, the modified effective Lagrangian allows one to study the black hole CFT in an expansion in powers of $d-6$ and $T_H-T$. At $T=T_H$, the sigma model is non-trivial for all $d>6$. It exhibits an enhanced $SU(2)$ symmetry, and is described by a non-abelian Thirring model with a radially dependent coupling. The resulting picture connects naturally to the results of [3-5], that relate Schwarzschild black holes in flat spacetime at large $d$ to the two dimensional black hole. We also discuss an analogous open string system, in which the black hole is replaced by a system of two separated D-branes connected by a throat. In this system, the asymptotic separation of the branes plays the role of the inverse temperature. At the critical separation, the system is described by a Kondo-type model, which again exhibits an enhanced $SU(2)$ symmetry. At large $d$, the brane system gives rise to the hairpin brane [6].