  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].
