String Scale Thermal Anti-de Sitter Spaces

TL;DR

This paper investigates finite temperature string theory in AdS_3 backgrounds, revealing a rich spectrum, symmetry breaking phenomena, and phase transitions, with implications for understanding string dynamics at the string scale.

Contribution

It provides a detailed analysis of string spectra, symmetry breaking, and phase transitions in string scale AdS_3 backgrounds, including derivation of the Hawking-Page transition.

Findings

Bulk spectrum includes continuum and Ramond-Ramond ground states.

Spontaneous breaking of conformal and R-charge conjugation symmetries.

Identification of the Hawking-Page transition in string theory.

Abstract

We study finite temperature string scale $AdS_3$ backgrounds. One background is $AdS_3 \times S^1 \times T^2$ in which the anti-de Sitter space-time and the circle are at the radius $\sqrt{\alpha'}$. Using path integral techniques, we show that the bulk spectrum includes a continuum of states as well as Ramond-Ramond ground states that agree with those of the symmetric orbifold of the two-torus after second quantization. We also examine the one-loop free energy of the background $AdS_3 \times S^1$ at curvature radius $\sqrt{2 \alpha'/3}$. In the space-time NSNS sector, the string theory spontaneously breaks conformal symmetry as well as R-charge conjugation symmetry. We prove that the minimum in the boundary energy is reached for a singly wound string. In the RR sector, we classify the infinite set of ground states with fractional R-charges. Moreover, we remark on the behaviour of critical temperatures as the curvature scale becomes smaller than the string scale. In an appendix, we derive the Hawking-Page transition in string theory by integrating a world sheet one-point function.