Thermodynamic behavior of IIA string theory on a pp-wave

TL;DR

This paper calculates the thermal free energy and Hagedorn temperature of IIA superstring theory on a pp-wave background, revealing universal thermal properties and consistency between operator and path integral methods.

Contribution

It provides the first complete agreement between operator and path integral calculations of free energy for IIA strings on a pp-wave, and shows universality with IIB string theory in the large  limit.

Findings

Free energy matches between operator and path integral methods.

Hagedorn temperature derived for IIA string on pp-wave.

Universal behavior observed in the   limit, aligning with IIB theory.

Abstract

We obtain the thermal one loop free energy and the Hagedorn temperature of IIA superstring theory on the pp-wave geometry which comes from the circle compactification of the maximally supersymmetric eleven dimensional one. We use both operator and path integral methods and find the complete agreement between them in the free energy expression. In particular, the free energy in the $\mu \to \infty$ limit is shown to be identical with that of IIB string theory on maximally supersymmetric pp-wave, which indicates the universal thermal behavior of strings in the large class of pp-wave backgrounds. We show that the zero point energy and the modular properties of the free energy are naturally incorporated into the path integral formalism.