  Recently, Diaconescu, Moore and Witten provided a nontrivial link between
K-theory and M-theory, by deriving the partition function of the Ramond-Ramond
fields of Type IIA string theory from an E8 gauge theory in eleven dimensions.
We give some relations between twisted K-theory and M-theory by adapting the
method of Diaconescu-Moore-Witten and Moore-Saulina. In particular, we
construct the twisted K-theory torus which defines the partition function, and
also discuss the problem from the E8 loop group picture, in which the
Dixmier-Douady class is the Neveu-Schwarz field. In the process of doing this,
we encounter some mathematics that is new to the physics literature. In
particular, the eta differential form, which is the generalization of the eta
invariant, arises naturally in this context. We conclude with several open
problems in mathematics and string theory.
