Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds

Understand

We develop quantization techniques for describing the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds M.

• Starting from a suitable Courant sigma-model on an open membrane with target space M, regarded as a topological sector of closed string dynamics in R-space, we derive a twisted Poisson sigma-model on the boundary of the membrane whose target space is the cotangent bundle T^*M and whose quasi-Poisson structure coincides with those previously proposed.
• We argue that from the membrane perspective the path integral over multivalued closed string fields in Q-space is equivalent to integrating over open strings in R-space.
• The corresponding boundary correlation functions reproduce Kontsevich's deformation quantization formula for the twisted Poisson manifolds.