Nonassociative geometry and twist deformations in non-geometric string theory

Understand

We describe nonassociative deformations of geometry probed by closed strings in non-geometric flux compactifications of string theory.

• We show that these non-geometric backgrounds can be geometrised through the dynamics of open membranes whose boundaries propagate in the phase space of the target space compactification, equiped with a twisted Poisson structure.
• The effective membrane target space is determined by the standard Courant algebroid over the target space twisted by an abelian gerbe in momentum space.
• Quantization of the membrane sigma-model leads to a proper quantization of the non-geometric background, which we relate to Kontsevich's formalism of global deformation quantization that constructs a noncommutative nonassociative star product on phase space.