((F, D1), D3) bound state, S-duality and noncommutative open string/Yang-Mills theory

TL;DR

This paper investigates the S-duality properties of noncommutative open string and Yang-Mills theories using a supergravity solution, revealing conditions under which S-duality relates different noncommutative theories and highlighting the complexity of their coupling behaviors.

Contribution

It provides a detailed analysis of decoupling limits and S-duality transformations for noncommutative theories in a supergravity framework, uncovering new relationships and limitations.

Findings

S-duality can relate NCOS to NCYM in certain limits.

S-duality of NCYM does not always produce NCOS, sometimes resulting in ordinary Yang-Mills.

The open string coupling relation is modified under S-duality, affecting the coupling strength.

Abstract

We study decoupling limits and S-dualities for noncommutative open string/ Yang-Mills theory in a gravity setup by considering an $SL(2,Z)$ invariant supergravity solution of the form ((F, D1), D3) bound state of type IIB string theory. This configuration can be regarded as D3-branes with both electric and magnetic fields turned on along one of the spatial directions of the brane and preserves half of the space-time supersymmetries of the string theory. Our study indicates that there exists a decoupling limit for which the resulting theory is an open string theory defined in a geometry with noncommutativity in both space-time and space-space directions. We study S-duality of this noncommutative open string (NCOS) and find that the same decoupling limit in the S-dual description gives rise to a space-space noncommutative Yang-Mills theory (NCYM). We also discuss independently the decoupling limit for NCYM in this D3 brane background. Here we find that S-duality of NCYM theory does not always give a NCOS theory. Instead, it can give an ordinary Yang-Mills with a singular metric and an infinitely large coupling. We also find that the open string coupling relation between the two S-duality related theories is modified such that S-duality of a strongly coupled open-string/Yang-Mills theory does not necessarily give a weakly coupled theory. The relevant gravity dual descriptions of NCOS/NCYM are also given.