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arxiv: 1211.0395 · v2 · pith:XIGJPP6Xnew · submitted 2012-11-02 · ✦ hep-th · math-ph· math.MP· math.QA· math.SG

Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds

classification ✦ hep-th math-phmath.MPmath.QAmath.SG
keywords manifoldsloopplecticquantizationspacesgroupoidstringtheory
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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.

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