On small black holes in string theory

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, TH, it can be described in terms of a generalized version of the Horowitz-Polchinski effective theory. For d ≥ 6, 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 TH − T. At T = TH, 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].