Non-Commutative Open (p,q)-String Theories

TL;DR

This paper develops an SL(2,Z)-covariant framework for noncommutative open (p,q)-string theories on D3- and D5-branes, extending the understanding of S-duality and providing new noncommutative theories related by duality transformations.

Contribution

It introduces an SL(2,Z)-covariant generalization of open string data for (p,q)-strings, enabling a unified study of noncommutative theories and their S-duals on D-branes.

Findings

Reproduces S-duality of NCYM and NCOS on D3-branes.

Constructs new noncommutative (p,q)-string theories S-dual to NCOS.

Uses supergravity duals to analyze the theories.

Abstract

In this paper we make an SL(2,Z)-covariant generalisation of the noncommutative theories, NCYM and NCOS on the D3-brane, and NCOS on the D5-brane in type IIB. Usually, the noncommutative theories are obtained by studying perturbative F-string theory, and the parameters governing the noncommutative theories are given by the open string data. The S-duality of NCYM and NCOS on the D3-brane has been seen by dualising the background, keeping the F-string under study fixed. We give an SL(2,Z)-covariant generalisation of the open string data relevant when one instead studies perturbative (p,q)-string theory. The S-duality of NCYM and NCOS on the D3-brane is reproduced by instead keeping the background fixed and studying different (p,q)-string theories. We also obtain new noncommutative open (p,q)-string theories on the D3-brane and the D5-brane which are S-dual to ordinary NCOS. The theories are studied using the supergravity duals of the D3-brane and the D5-brane, corresponding to a probe brane in the relevant background.