On the Deformation Quantization Description of Matrix Compactifications

TL;DR

This paper introduces a deformation quantization framework for matrix theory compactifications, extending noncommutative Yang-Mills theories to curved spaces with non-constant B-fields using Fedosov's geometry.

Contribution

It provides a novel geometric approach to generalize noncommutative Yang-Mills theories on curved spaces with variable B-fields via Fedosov's deformation quantization.

Findings

Framework extends Moyal B-deformation to curved spaces

Utilizes Fedosov's geometry for deformation quantization

Enables noncommutative descriptions with non-constant B-fields

Abstract

Matrix theory compactifications on tori have associated Yang-Mills theories on the dual tori with sixteen supercharges. A noncommutative description of these Yang-Mills theories based in deformation quantization theory is provided. We show that this framework allows a natural generalization of the `Moyal B-deformation' of the Yang-Mills theories to non-constant background B-fields on curved spaces. This generalization is described through Fedosov's geometry of deformation quantization.