Groupoids, loop spaces and quantization of 2-plectic manifolds

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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.
Original languageEnglish
Number of pages72
JournalReviews in Mathematical Physics
Volume25
Issue number3
DOIs
Publication statusPublished - Apr 2013

Keywords

  • hep-th
  • math-ph
  • math.MP
  • math.QA
  • math.SG

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