Discrete Torsion and WZW Orbifolds

TL;DR

This paper provides a geometric interpretation of discrete torsion in WZW orbifolds, linking algebraic choices to geometric data like subgroup actions and H-field connections, and illustrating with lens spaces.

Contribution

It introduces a geometric framework for understanding discrete torsion in WZW orbifolds, connecting algebraic and geometric perspectives.

Findings

Discrete torsion relates to subgroup actions and H-field connections.

Different quotient spaces correspond to different discrete torsion choices.

Application to generalized lens spaces L(n,p).

Abstract

We propose a geometrical interpretation for the discrete torsion appearing in the algebraic formulation of quotients of WZW models by discrete abelian subgroups. Part of the discrete torsion corresponds to the choice of action of the subgroup, yielding different quotient spaces. Another part corresponds to the set of different choices of connection for the H field in each of these spaces. The former is for instance used to describe generalized lens spaces L(n,p).