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.
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