Nonassociative tori and applications to T-duality

In this paper, we initiate the study of C*-algebras A endowed with a twisted action of a locally compact abelian Lie group G, and we construct a twisted crossed product A x G, which is in general a nonassociative, noncommutative, algebra. The duality properties of this twisted crossed product algebra are studied in detail, and are applied to T-duality in Type II string theory to obtain the T-dual of a general principal torus bundle with general H-flux, which we will argue to be a bundle of noncommutative, nonassociative tori. Nonassociativity is interpreted in the context of monoidal categories of modules. We also show that this construction of the T-dual includes the other special cases already analysed in a series of papers.