Analogues of Discrete Torsion for the M-Theory Three-Form

TL;DR

This paper explores the concept of discrete torsion analogues in M-theory, focusing on the three-form potential and how orbifold group actions are classified by cohomology, with implications for membrane phases.

Contribution

It introduces a derivation of discrete torsion analogues for the M-theory three-form and analyzes their classification and invariance properties.

Findings

Orbifold group actions on the C field classified by H^3(G, U(1))

Computed phases for membrane actions in twisted sectors

Phases are invariant under SL(3,Z) transformations

Abstract

In this article we shall outline a derivation of the analogue of discrete torsion for the M-theory three-form potential. We find that some of the differences between orbifold group actions on the C field are classified by H^3(G, U(1)). We also compute the phases that the low-energy effective action of a membrane on T^3 would see in the analogue of a twisted sector, and note that they are invariant under the obvious SL(3,Z) action.