Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class

TL;DR

This paper constructs explicit twisted K-theory classes on product manifolds with decomposable Dixmier-Douady classes using a quantum field theory model, extending previous work on twisted K-theory in this specific setting.

Contribution

It provides an explicit construction method for twisted K-theory classes in the case of decomposable Dixmier-Douady classes using quantum field theory techniques.

Findings

Explicit construction of twisted K-theory classes for decomposable twists.

Extension of quantum field theory models to product manifolds.

Connection to supersymmetric Wess-Zumino-Witten models.

Abstract

Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is dis- cussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral one form on T and an integral class in H2(M,Z). This case was studied some time ago by V. Mathai, R. Melrose, and I.M. Singer. Our aim is to give an explicit construction for the twisted K-theory classes using a quantum field theory model, in the same spirit as the supersymmetric Wess-Zumino-Witten model is used for constructing (equivariant) twisted K-theory classes on compact Lie groups.