Winding Tachyons and Stringy Black Holes

Abstract

We study string theory on ${\mathbb{R}}^d\times {\mathbb{S}}^1$. For applications to thermodynamics, the circumference of the ${\mathbb{S}}^1$ is the inverse temperature, $\beta$. We show that for $d=6$, the low energy effective field theory at the inverse Hagedorn temperature, $\beta ={\beta }_H$, has a one parameter family of normalizable spherically symmetric solutions that break the winding symmetry around the ${\mathbb{S}}^1$. The resulting backgrounds exhibit an enhanced symmetry, with the symmetry breaking pattern $SU(2{)}_L\times SU(2{)}_R\to SU(2{)}_{\mathrm{diagonal}}$. The effective field theory analysis of these backgrounds is reliable for some range of parameters. More generally, they are described by a worldsheet CFT, which corresponds to the free theory on ${\mathbb{R}}^6\times {\mathbb{S}}^1$ perturbed by a non-abelian Thirring deformation with an $r$-dependent coupling. We propose that, in a certain scaling limit, string theory in these backgrounds is described by the $SL(2,\mathbb{R})/U(1)$ cigar, and provides a thermodynamic description of weakly coupled highly excited fundamental strings. We also discuss the relation of these backgrounds to Euclidean black holes with near-Hagedorn Hawking temperature, and possible generalizations to other $d$.

33 pages, 8 figures