Orientifolds of Matrix theory and Noncommutative Geometry

TL;DR

This paper explores explicit solutions for orientifolds of Matrix theory on noncommutative tori, utilizing projective modules to analyze twisted gauge bundles and boundary conditions that define dual space geometry.

Contribution

It provides a detailed construction of orientifold solutions in noncommutative geometry using Connes, Douglas, and Schwarz's approach, extending understanding of gauge theories on quotient spaces.

Findings

Explicit solutions for orientifolds on noncommutative tori are derived.

The study characterizes twisted gauge bundles and boundary conditions on quotient spaces.

Connections between noncommutative geometry and string theory orientifolds are clarified.

Abstract

We study explicit solutions for orientifolds of Matrix theory compactified on noncommutative torus. As quotients of torus, cylinder, Klein bottle and M\"obius strip are applicable as orientifolds. We calculate the solutions using Connes, Douglas and Schwarz's projective module solution, and investigate twisted gauge bundle on quotient spaces as well. They are Yang-Mills theory on noncommutative torus with proper boundary conditions which define the geometry of the dual space.