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

Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed 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 H-2(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.