Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds

Christian Saemann; Richard J. Szabo

doi:10.1142/s0129055x13300057

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arXiv · 1211.0395

Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds

Christian Saemann·Richard J. Szabo

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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.

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Christian Saemann, Richard J. Szabo. 2012-11-26. Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds. https://doi.org/10.1142/s0129055x13300057

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