Noncommutative gerbes and deformation quantization

TL;DR

This paper introduces noncommutative gerbes via star products, explores their role in deformation quantization of twisted Poisson structures, and applies these concepts to the noncommutative modeling of D-branes with complex background fields.

Contribution

It defines noncommutative gerbes within the star product framework and connects them to twisted Poisson structures in deformation quantization.

Findings

Explicit realization of quantized twisted Poisson structures

Application to noncommutative D-brane descriptions

Advancement in noncommutative geometry methods

Abstract

We define noncommutative gerbes using the language of star products. Quantized twisted Poisson structures are discussed as an explicit realization in the sense of deformation quantization. Our motivation is the noncommutative description of D-branes in the presence of topologically non-trivial background fields.