Abstract
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.
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Ashok, S.K., Troost, J. String scale thermal anti-de Sitter spaces. J. High Energ. Phys. 2021, 24 (2021). https://doi.org/10.1007/JHEP05(2021)024
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DOI: https://doi.org/10.1007/JHEP05(2021)024