English

Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds

High Energy Physics - Theory 2013-08-26 v2 Mathematical Physics math.MP Quantum Algebra Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.1211.0395,
  title  = {Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds},
  author = {Christian Saemann and Richard J. Szabo},
  journal= {arXiv preprint arXiv:1211.0395},
  year   = {2013}
}

Comments

71 pages, v2: references added

R2 v1 2026-06-21T22:32:01.192Z