Branes, Quantization and Fuzzy Spheres

TL;DR

This paper introduces generalized quantization axioms for Nambu-Poisson manifolds, enabling geometric interpretation of n-Lie algebras, and applies them to construct quantum spaces like fuzzy spheres relevant to M-brane dynamics.

Contribution

It proposes new axioms for quantization of Nambu-Poisson manifolds and extends Berezin-Toeplitz quantization to create quantum spaces such as fuzzy spheres.

Findings

Extended Berezin-Toeplitz quantization to fuzzy spheres

Proposed axioms for quantizing Nambu-Poisson manifolds

Initial steps towards rigorous quantization of 2-plectic manifolds

Abstract

We propose generalized quantization axioms for Nambu-Poisson manifolds, which allow for a geometric interpretation of n-Lie algebras and their enveloping algebras. We illustrate these axioms by describing extensions of Berezin-Toeplitz quantization to produce various examples of quantum spaces of relevance to the dynamics of M-branes, such as fuzzy spheres in diverse dimensions. We briefly describe preliminary steps towards making the notion of quantized 2-plectic manifolds rigorous by extending the groupoid approach to quantization of symplectic manifolds.