BPS Solutions of Noncommutative Gauge Theories in Four and Eight Dimensions

TL;DR

This paper constructs explicit solutions to 1/4 BPS equations in eight-dimensional noncommutative Yang-Mills theory, revealing their interpretation as bound states of D-branes and analyzing the moduli space structure.

Contribution

It introduces a noncommutative ADHM-like construction for 8D BPS solutions and explores their topological charges and moduli space metrics.

Findings

Solutions represent D0-D4-D8 bound states with B-field

Explicit moduli space metric for U(2) one-instanton

Connection between solutions and topological charges

Abstract

We study the 1/4 BPS equations in the eight dimensional noncommutative Yang-Mills theory found by Bak, Lee and Park. We explicitly construct some solutions of the 1/4 BPS equations using the noncommutative version of the ADHM-like construction in eight dimensions. From the calculation of topological charges, we show that our solutions can be interpreted as the bound states of the $D0$-$D4$-$D8$ with a $B$-field. We also discuss the structure of the moduli space of the 1/4 BPS solutions and determine the metric of the moduli space of the U(2) one-instanton in four and eight dimensions.