Modular invariant partition functions for non-compact G/Ad(H) models

TL;DR

This paper develops a method to construct modular invariant partition functions for non-compact G/Ad(H) models by regularizing divergent characters, enabling consistent analysis of their spectral properties.

Contribution

It introduces a spectrum for gauged non-compact G/Ad(H) WZNW models, including spectrally flowed modules, and demonstrates their characters' modular invariance after regularization.

Findings

Characters transform linearly under modular transformations

Partition functions can be made modular invariant

Regularization of divergent characters is feasible

Abstract

We propose a spectrum for a class of gauged non-compact G/Ad(H) WZNW models, including spectrally flowed images of highest, lowest, and mixed extremal weight modules. These are combined into blocks whose characters, due to the Lorentzian signature of the target space, are divergent and treated as formal expressions in need of regularisation. Assuming that this is possible, we show that these extended characters transform linearly under modular transformations, and can be used to write down modular invariant partition functions.