Superstrings in Thermal Anti-de Sitter Space

TL;DR

This paper analyzes the thermal free energy of superstring theory in three-dimensional anti-de Sitter space, confirming the Hilbert space structure, exploring boundary conformal dimensions, and revealing modular properties of the partition function.

Contribution

It extends previous calculations to superstrings in AdS3, classifies R-R ground states, and constructs their second quantized partition function with modular features.

Findings

Casimir of discrete representations in a half-open interval

Lower bounds on boundary conformal dimensions from bulk analysis

Partition function exhibits intriguing modular properties

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.