Discrete Torsion and Shift Orbifolds

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.