3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua

Understand

We consider the geometric and non-geometric faces of closed string vacua arising by T-duality from principal torus bundles with constant H-flux and pay attention to their double phase space description encompassing all toroidal coordinates, momenta and their dual on equal footing.

• We construct a star-product algebra on functions in phase space that is manifestly duality invariant and substitutes for canonical quantization.
• The 3-cocycles of the Abelian group of translations in double phase space are seen to account for non-associativity of the star-product.
• We also provide alternative cohomological descriptions of non-associativity and draw analogies with the quantization of point-particles in the field of a Dirac monopole or other distributions of magnetic charge.