Dp-D(p+4) in Noncommutative Yang-Mills

TL;DR

This paper constructs anti-self-dual instanton solutions in noncommutative Yang-Mills theory using ADHM, interprets them within the IIB matrix model as D-brane systems, and explores their moduli space and multi-instanton configurations.

Contribution

It provides explicit anti-self-dual instanton solutions in noncommutative Yang-Mills theory and interprets them as D-brane systems in the IIB matrix model, including multi-instanton solutions.

Findings

Solutions are constructed via ADHM in noncommutative space.

The solutions are interpreted as Dp-D(p+4) brane systems.

Even at moduli space singularities, gauge fields remain non-singular.

Abstract

An anti-self-dual instanton solution in Yang-Mills theory on noncommutative ${\R}^4$ with an anti-self-dual noncommutative parameter is constructed. The solution is constructed by the ADHM construction and it can be treated in the framework of the IIB matrix model. In the IIB matrix model, this solution is interpreted as a system of a Dp-brane and D(p+4)-branes, with the Dp-brane dissolved in the worldvolume of the D(p+4)-branes. The solution has a parameter that characterises the size of the instanton. The zero of this parameter corresponds to the singularity of the moduli space. At this point, the solution is continuously connected to another solution which can be interpreted as a system of a Dp-brane and D(p+4)-branes, with the Dp-brane separated from the D(p+4)-branes. It is shown that even when the parameter of the solution comes to the singularity of the moduli space, the gauge field itself is non-singular. A class of multi-instanton solutions is also constructed.