Closed Bosonic String Partition Function in Time Independent Exact PP-Wave Background

TL;DR

This paper investigates the modular invariance of the one-loop partition function of closed bosonic strings in four-dimensional pp-wave backgrounds, highlighting conditions under which invariance is preserved or broken and proposing ways to restore it.

Contribution

It analyzes the effects of axion fields on modular invariance in string theory within pp-wave backgrounds and suggests modifications beyond the light-cone gauge to maintain symmetry.

Findings

Partition function is modular invariant without axion.

Axion fields break modular invariance.

Introducing twists beyond the light-cone gauge can restore invariance.

Abstract

The modular invariance of the one-loop partition function of the closed bosonic string in four dimensions in the presence of certain homogeneous exact pp-wave backgrounds is studied. In the absence of an axion field the partition function is found to be modular invariant. In the presence of an axion field modular invariace is broken. This can be attributed to the light-cone gauge which breaks the symmetry in the $\sigma$-, $t$-directions. Recovery of this broken modular invariance suggests the introduction of twists in the world-sheet directions. However, one needs to go beyond the light-cone gauge to introduce such twists.