String scale thermal anti-de Sitter spaces

We study finite temperature string scale AdS3 backgrounds. One background is AdS3 × S1 × T 2 in which the anti-de Sitter space-time and the circle are at the radius $$ \sqrt{\alpha^{\prime }} $$ . 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 AdS3 × S1 at curvature radius $$ \sqrt{2{\alpha}^{\prime }/3} $$ . 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.