Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds

Understand

We describe the quantization of 2-plectic manifolds as they arise in the context of the quantum geometry of M-branes and non-geometric flux compactifications of closed string theory.

• We review the groupoid approach to quantizing Poisson manifolds in detail, and then extend it to the loop spaces of 2-plectic manifolds, which are naturally symplectic manifolds.
• In particular, we discuss the groupoid quantization of the loop spaces of R^3, T^3 and S^3, and derive some interesting implications which match physical expectations from string theory and M-theory.