Abstract
We revisit the calculation of the thermal free energy for string theory in three-dimensional anti-de Sitter spacetime with Neveu-Schwarz-Neveu-Schwarz flux. The path integral calculation is exploited to confirm the off-shell Hilbert space and we find that the Casimir of the discrete representations of the isometry group takes values in a half-open interval. We extend the free energy calculation to the case of superstrings, calculate the boundary toroidal twisted partition function in the Ramond-Ramond sector, and prove lower bounds on the boundary conformal dimension from the bulk perspective. We classify Ramond-Ramond ground states and construct their second quantized partition function. The partition function exhibits intriguing modular properties.
Highlights
Holography is a conjectured property of quantum gravity
The strongest support for the duality has been gathered in string theory backgrounds with extended supersymmetry
The string theory we study is exceptional in that all tree level higher order curvature corrections in the inverse string tension expansion are under exact control
Summary
Holography is a conjectured property of quantum gravity. The claim is strongly substantiated in spacetimes with a negative cosmological constant by the anti-de Sitter/conformal field theory correspondence [1]. We revisit the calculation of the free energy of bosonic string theory in thermal three-dimensional anti-de Sitter space-time [2]. The spectrum of bosonic string theory in AdS3 was determined in [3] and was confirmed through a path integral calculation on thermal AdS3 [2]. We extend the free energy calculation to superstring theory and apply it to the determination of all boundary Ramond-Ramond ground states. Our calculation takes place in a thermally compactified global anti-de Sitter space-time, with supersymmetric boundary conditions along the circle. The path integral calculation proves that the spectrum of boundary chiral primaries determined in [4, 5] is complete.
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