Nonassociative Tori and Applications to T-Duality
By P. Bouwknegt, K. Hannabuss, Varghese Mathai. 2004
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In this paper, we initiate the study of C*-algebras endowed with a twisted action of a locally compact abelian Lie group , and we construct a twisted crossed product , 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.
Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/c93aa4a5ce99123a17df7c86d8b7b6a0e2815724
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Citations in the corpus
- Duality Symmetric String and M-Theory (2013, background): “Space limitations prevent us discussing in any detail a number of developments related to the contents of this chapter including21: the structure of large (finite) DFT gauge transformations [194, 195], the the matrix theory perspective of non-geometric fluxes [196, 197]; further perspectives on non-”
- Membrane sigma-models and quantization of non-geometric flux backgrounds (2012, methodology): “This description of the Q-space is consistent with its description from [14] as a fibration of stabilized noncommutative two-tori T(2)θ, with Poisson bivector θ varying over the base S 1; low-energy effective open string constructions are given in [28, 32], where the noncommutative fibration is rega”
- SU(3) × SU(3) compactification and mirror duals of magnetic fluxes (2006, background): “Instead, following recent ideas generalizing the notion of a string background, one must consider “non-geometrical” compactifications [22]–[42].”
- T-duality, generalized geometry and non-geometric backgrounds (2008, background): “For backgrounds with d isometries, since the T-duality group O(d, d) is much larger than the group of diffeomorphisms, it is not surprising that the action of T-duality can be more interesting and complicated [12].”