I will discuss the worldsheet sigma-model whose target space is the d+1 dimensional Euclidean Schwarzschild black hole. I will 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 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 that expected for a Schwarzchild black hole at large d, where an SL(2)/U(1) cigar CFT emerges.
I will 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.