Discrete Torsion

TL;DR

This paper explains discrete torsion as choices of orbifold group actions on the B field, deriving classifications, phases, and D-brane descriptions, and introduces new degrees of freedom called shift orbifolds.

Contribution

It provides a simplified derivation of discrete torsion classification, phases, and D-brane descriptions, and introduces shift orbifolds as additional degrees of freedom.

Findings

Derived classification H^2(G, U(1)) for discrete torsion

Connected discrete torsion phases to string loop partition functions

Identified shift orbifolds as new degrees of freedom in orbifold actions

Abstract

In this article we explain discrete torsion. Put simply, discrete torsion is the choice of orbifold group action on the B field. We derive the classification H^2(G, U(1)), we derive the twisted sector phases appearing in string loop partition functions, we derive M. Douglas's description of discrete torsion for D-branes in terms of a projective representation of the orbifold group, and we outline how the results of Vafa-Witten fit into this framework. In addition, we observe that additional degrees of freedom (known as shift orbifolds) appear in describing orbifold group actions on B fields, in addition to those classified by H^2(G, U(1)), and explain how these new degrees of freedom appear in terms of twisted sector contributions to partition functions and in terms of orbifold group actions on D-brane worldvolumes. This paper represents a technically simplified version of prior papers by the author on discrete torsion. We repeat here technically simplified versions of results from those papers, and have included some new material.