Thermal Partition Function of Superstring on Compactified PP-Wave

TL;DR

This paper computes the thermal partition function of superstring theory on a compactified pp-wave background using operator and path-integral methods, revealing the role of winding modes and the DLCQ limit.

Contribution

It provides a detailed comparison of operator and path-integral calculations of the thermal partition function, highlighting the effects of winding modes and DLCQ in a pp-wave background.

Findings

Operator formalism yields finite, physical state contributions.

Path-integral approach shows modular invariance with winding modes.

Winding contributions vanish in the non-DLCQ limit.

Abstract

We study the thermal partition function of superstring on the pp-wave background with the circle compactification along a transverse direction. We calculate it in the two ways: the operator formalism and the path-integral calculation. The former gives the finite result with no subtlety of the Wick rotation, which only contains the contributions of physical states. On the other hand, the latter yields the manifestly modular invariant expression, even though we only have the winding modes along the transverse circle (no Kaluza-Klein excitations). We also check the equivalence of these two analyses. The DLCQ approach makes the path-integration quite easy. Remarkably, we find that the contributions from the transverse winding sectors disappear in the non-DLCQ limit, while they indeed contribute in the DLCQ model, depending non-trivially on the longitudinal quantum numbers.