Quantization of 2-Plectic Manifolds

TL;DR

This paper extends quantization axioms to 2-plectic manifolds, proposing a novel approach using 3-algebra models and groupoid methods, with implications for quantum M-branes and nonassociative spacetime geometry.

Contribution

It introduces a new framework for quantizing 2-plectic manifolds using 3-algebra models and groupoid techniques, linking to quantum M-branes and nonassociative geometry.

Findings

Quantum 2-plectic spaces as stable solutions in 3-algebra models

Application of groupoid approach to 2-plectic quantization

Insights into nonassociative spacetime deformation

Abstract

We describe an extension of the axioms of quantization to the case of 2-plectic manifolds. We show how such quantum spaces can be obtained as stable classical solutions in a zero-dimensional 3-algebra reduced model obtained by dimensional reduction of the Bagger-Lambert-Gustavsson theory. We demonstrate that the groupoid approach to geometric quantization proposed by Hawkins and others can be useful for quantizing 2-plectic manifolds. We discuss our results in the context of recent developments in the quantum geometry of M-branes, and in the nonassociative deformation of spacetime induced by closed strings in the presence of a 2-plectic form.