Discrete Torsion and Shift Orbifolds

TL;DR

This paper explores the relationship between discrete torsion and shift orbifolds in string theory, revealing new dualities and clarifying how momentum shifts relate to discrete torsion in orbifold constructions.

Contribution

It demonstrates the connection between momentum lattice shifts and discrete torsion, and uncovers the M theory dual of IIA discrete torsion involving C field shift orbifolds.

Findings

Discrete torsion relates to momentum/translation shifts in orbifolds.

The M theory dual of IIA discrete torsion involves C field shift orbifolds.

New duality between IIA discrete torsion and M theory C field shifts.

Abstract

In this paper we make two observations related to discrete torsion. First, we observe that an old obscure degree of freedom (momentum/translation shifts) in (symmetric) string orbifolds is related to discrete torsion. We point out how our previous derivation of discrete torsion from orbifold group actions on B fields includes these momentum lattice shift phases, and discuss how they are realized in terms of orbifold group actions on D-branes. Second, we describe the M theory dual of IIA discrete torsion, a duality relation to our knowledge not previously understood. We show that IIA discrete torsion is encoded in analogues of the shift orbifolds above for the M theory C field.