From Horowitz -- Polchinski to Thirring and Back

We propose a new approach for studying $d+1$ dimensional Euclidean Schwarzschild black holes with Hawking temperature near the Hagedorn temperature and Horowitz-Polchinski solutions. The worldsheet theory that describes some of these backgrounds is strongly coupled. We use its underlying affine $SU(2)_L\times SU(2)_R$ symmetry to continue to weak coupling, by varying the level of the current algebra from the small value relevant for black holes and HP solutions to a large value. In this limit, one can describe the dynamics by a solvable effective field theory, and the non-geometric features of the original problem are geometrized. The resulting construction is closely related to previous work on the non-abelian Thirring model, and sheds light on both problems.