Superstrings in thermal anti-de Sitter space

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.

Automated summary

The study revisited the calculation of the thermal free energy in three-dimensional anti-de Sitter spacetime with Neveu-Schwarz-Neveu-Schwarz flux and extended it to superstrings. The boundary toroidal twisted partition function in the Ramond-Ramond sector was calculated and lower bounds on the boundary conformal dimension were proven from the bulk perspective. The study also classified Ramond-Ramond ground states and constructed their second quantized partition function, revealing intriguing modular properties.