On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations

TL;DR

This paper demonstrates how various noncommutative integrable equations can be derived from noncommutative anti-self-dual Yang-Mills equations, providing insights into their physical interpretations in string theory and D-brane systems.

Contribution

It shows the derivation of multiple noncommutative integrable equations from anti-self-dual Yang-Mills equations, supporting noncommutative Ward's conjecture and linking to D-brane physics.

Findings

Derivation of noncommutative KdV, NLS, N-wave, Davey-Stewartson, KP equations from Yang-Mills

U(1) gauge group plays a crucial role in noncommutative extensions

Implications for D-brane configurations in string theory

Abstract

In this paper, we show that various noncommutative integrable equations can be derived from noncommutative anti-self-dual Yang-Mills equations in the split signature, which include noncommutative versions of Korteweg-de Vries, Non-Linear Schroedinger, N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations. U(1) part of gauge groups for the original Yang-Mills equations play crucial roles in noncommutative extension of Mason-Sparling's celebrated discussion. The present results would be strong evidences for noncommutative Ward's conjecture and imply that these noncommutative integrable equations could have the corresponding physical pictures such as reduced configurations of D0-D4 brane systems in open N=2 string theories. Possible applications to the D-brane dynamics are also discussed.