Noncommutative Differential Calculus for D-brane in Non-Constant B Field Background

TL;DR

This paper develops a noncommutative differential calculus framework to extend key string theory and gauge theory results from constant to non-constant B field backgrounds, broadening the understanding of D-branes in complex environments.

Contribution

It introduces a noncommutative differential calculus for Poisson manifolds and generalizes important string theory results to non-constant B field backgrounds.

Findings

Generalized Seiberg-Witten map to non-constant B fields

Extended Dirac-Born-Infeld action in non-constant backgrounds

Applied calculus to open string quantization with H=0

Abstract

In this paper we try to construct noncommutative Yang-Mills theory for generic Poisson manifolds. It turns out that the noncommutative differential calculus defined in an old work is exactly what we need. Using this calculus, we generalize results about the Seiberg-Witten map, the Dirac-Born-Infeld action, the matrix model and the open string quantization for constant B field to non-constant background with H=0.