Twisted equivariant quasi-elliptic cohomology and M-brane charge

TL;DR

This paper develops a twisted quasi-elliptic cohomology theory as a K-theory of loop spaces, establishing its properties, constructing a Chern character, and computing examples related to M-brane charges, linking to string theory conjectures.

Contribution

It introduces a new twisted quasi-elliptic cohomology framework, extending existing theories and connecting to M-brane charge computations in string theory.

Findings

Constructed a twisted quasi-elliptic cohomology theory.

Established properties including restriction, change-of-group, and induction.

Computed examples related to M-brane charge and D-brane charge enhancements.

Abstract

In this paper we construct a twisted version of quasi-elliptic cohomology. This theory can be constructed as a K-theory of a loop space. After establishing basic properties of the theory, including restriction, change-of-group and induction maps, we construct the Chern character map. And we compute the twisted quasi-elliptic cohomology theories of representation 4-spheres acted by the finite subgroups of SU(2), which, as conjectured by Sati and Schreiber, can produce good observables on M-brane charge in a Tate-elliptic enhancement of D-brane charge in twisted equivariant K-theory.