Noncommutative Geometry From Strings and Branes

TL;DR

This paper demonstrates how noncommutative geometry arises from string theory and branes, specifically through the quantization of open strings on D-membranes with background fields, and explores related spectrum and transformation properties.

Contribution

It establishes a direct link between noncommutative torus compactification and string quantization, introducing a new transformation property of radii under $SL(2,Z)_N$.

Findings

Derivation of noncommutative torus from string quantization

Calculation of BPS spectrum using string theory and DBI action

Identification of new $SL(2,Z)_N$ transformation property

Abstract

Noncommutative torus compactification of Matrix model is shown to be a direct consequence of quantization of the open strings attached to a D-membrane with a non-vanishing background $B$ field. We calculate the BPS spectrum of such a brane system using both string theory results and DBI action. The DBI action leads to a new transformation property of the compactification radii under the $SL(2,Z)_N$ transformations.