On deformation quantization of Dirac structures

TL;DR

This paper develops a method for deforming Dirac structures into stacks of algebroids, advancing the understanding of transverse deformation quantization for foliated manifolds.

Contribution

It introduces a quantization framework for Dirac structures, specifically for their formal deformations of regular types, using stacks of algebroids as per Kontsevich.

Findings

Provides a new approach to transverse deformation quantization

Connects Dirac structures with stacks of algebroids

Advances the mathematical understanding of foliated manifolds

Abstract

Motivated by the problem of transverse deformation quantization of foliated manifolds, we describe a quantization of Dirac structures (more precisely, of those that are formal deformations of regular ones) to stacks of algebroids in the sense of Kontsevich.