Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds

Abstract

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.

71 pages, v2: references added

References in corpus (3)

• n-ary algebras: a review with applications
• Quantized Nambu-Poisson Manifolds and n-Lie Algebras
• Constructing Self-Dual Strings

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