String Scale Thermal Anti-de Sitter Spaces

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.