Winding Tachyons and Stringy Black Holes

TL;DR

This paper explores string theory on a space with a circle, revealing new solutions at the Hagedorn temperature that break winding symmetry, connect to black hole physics, and are described by a worldsheet conformal field theory and the $SL(2, ext{R})/U(1)$ cigar model.

Contribution

It identifies a family of solutions at the Hagedorn temperature that break winding symmetry and links string backgrounds to black hole models via the $SL(2, ext{R})/U(1)$ cigar CFT.

Findings

Existence of a one-parameter family of solutions at the Hagedorn temperature.

Symmetry breaking pattern from $SU(2)_L\times SU(2)_R$ to $SU(2)_{\text{diagonal}}$.

Connection between string backgrounds and Euclidean black holes near the Hagedorn temperature.

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 $SU(2)_L\times SU(2)_R\to SU(2)_{\rm diagonal}$. 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 $d$.