A Note on the Equivalence of Vafa's and Douglas's Picture of Discrete Torsion

TL;DR

This paper demonstrates that Vafa's and Douglas's definitions of discrete torsion are equivalent for nonabelian group actions on arbitrary genus worldsheets, unifying two perspectives in string theory.

Contribution

It proves the equivalence of Vafa's and Douglas's discrete torsion definitions for general nonabelian groups and arbitrary genus worldsheets.

Findings

Vafa's and Douglas's definitions coincide for nonabelian groups

The equivalence holds for arbitrary genus worldsheets

Unifies two approaches to discrete torsion in string theory

Abstract

For a general nonabelian group action and an arbitrary genus worldsheet we show that Vafa's old definition of discrete torsion coincides with Douglas's D-brane definition of discrete torsion associated to projective representations.