Noncommutative Gauge Theories from Deformation Quantization

TL;DR

This paper develops a framework for noncommutative gauge theories using Fedosov's deformation quantization, unifying background fields and gauge symmetries in string theory contexts.

Contribution

It introduces a universal gauge theory based on the Weyl bundle, connecting noncommutative gauge theories with deformation quantization on symplectic manifolds.

Findings

Constructs noncommutative gauge theories from Fedosov's Weyl bundle.

Shows the universality of gauge fields and symmetries in this framework.

Links background B-fields and noncommutative field strengths through a universal structure.

Abstract

We construct noncommutative gauge theories based on the notion of the Weyl bundle, which appears in Fedosov's construction of deformation quantization on an arbitrary symplectic manifold. These correspond to D-brane worldvolume theories in non-constant B-field and curved backgrounds in string theory. All such theories are embedded into a "universal" gauge theory of the Weyl bundle. This shows that the combination of a background field and a noncommutative field strength has universal meaning as a field strength of the Weyl bundle. We also show that the gauge equivalence relation is a part of such a "universal" gauge symmetry.