Matrix Theory on Noncommutative Torus

TL;DR

This paper explores the compactification of Matrix theory on tori with background fields, demonstrating how noncommutative geometry naturally arises in this context through explicit construction.

Contribution

It provides a concrete construction of Matrix theory compactification on noncommutative tori, extending previous work by Douglas, Hull, and Taylor.

Findings

Noncommutative geometry appears on tori with background antisymmetric tensor fields.

Explicit construction of Matrix theory compactification on noncommutative tori.

Connections to previous theoretical frameworks are established.

Abstract

We consider the compactification of Matrix theory on tori with background antisymmetric tensor field. Douglas and Hull have recently discussed how noncommutative geometry appears on the tori. In this paper, we demonstrate the concrete construction of this compactification of Matrix theory in a similar way to that previously given by Taylor.