String Scale Thermal Anti-de Sitter Spaces

Abstract

We study finite temperature string scale $Ad{S}_3$ backgrounds. One background is $Ad{S}_3\times S^1\times T^2$ 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 $Ad{S}_3\times S^1$ 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.

arXiv comment20 pages

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Cited by in corpus (3)

• String Stars in Anti de Sitter Space
• Asymptotically Free AdS3/CFT2
• The $Ad{S}_3\times S^1$ Chiral Ring