Noncommutative Gauge Theories in Matrix Theory

TL;DR

This paper develops a framework for formulating noncommutative gauge theories within Matrix theory compactified on quotient spaces, incorporating twisted group algebras and orientifolds.

Contribution

It introduces a general method to construct noncommutative gauge theories from Matrix theory on quotient spaces using twisted group algebras.

Findings

Provides a solution to quotient conditions in Matrix theory.

Characterizes noncommutative gauge theories via twisted group algebras.

Extends framework to include orientifolds.

Abstract

We present a general framework for Matrix theory compactified on a quotient space R^n/G, with G a discrete group of Euclidean motions in R^n. The general solution to the quotient conditions gives a gauge theory on a noncommutative space. We characterize the resulting noncommutative gauge theory in terms of the twisted group algebra of G associated with a projective regular representation. Also we show how to extend our treatments to incorporate orientifolds.