Thermal Amplitudes in DLCQ Superstrings on PP-Waves

TL;DR

This paper computes the thermal partition function of DLCQ superstrings on pp-wave backgrounds, demonstrating modular invariance, analyzing Hagedorn temperature, and exploring open-closed string duality, extending to backgrounds with various fluxes.

Contribution

It provides a detailed derivation of the thermal partition function for DLCQ superstrings on pp-wave backgrounds, including modular invariance and duality, and extends the analysis to more general flux backgrounds.

Findings

Derived a modular invariant thermal partition function.

Confirmed open-closed string duality in the thermal setting.

Extended thermodynamical analysis to backgrounds with RR and NSNS flux.

Abstract

We calculate the thermal partition function of DLCQ superstring on the maximally supersymmetric pp-wave background, which is realized as the Penrose limit of orbifolded $AdS_5\times S^5$ and known to be dual to the $\mathcal{N}=2$ ``large'' quiver gauge theory as shown by S. Mukhi, M. Rangamani and E. Verlinde, hep-th/0204147. Making use of the path-integral technique, we derive the manifestly modular invariant expression and show the equivalence with the free energy of second quantized free superstring on this background. The ``virtual strings'' wound around the temporal circle play essential roles for realizing the modular invariance and for a simple analysis on the Hagedorn temperature. We also calculate the thermal one-loop amplitudes of open strings under the various backgrounds of the supersymmetric time-like and Euclidean D-branes, and confirm the existence of correct open-closed string duality. Furthermore, we extend these thermodynamical analysis to the 6-dimensional DLCQ pp-waves with general RR and NSNS flux. These superstring vacua are similarly derived from the supersymmetric (half SUSY) and non-supersymmetric orbifolds of $AdS_3 \times S^3 \times M^4$ ($M^4 =T^4 $ or $K3$) by the appropriate Penrose limits, giving rise to the SUSY enhancement as in the case of orbifolded $AdS_5 \times S^5$.