BPS equations in Six and Eight Dimensions

TL;DR

This paper systematically classifies BPS equations in six and eight-dimensional supersymmetric Yang-Mills theories, identifying preserved supersymmetry fractions and applying results to explicit configurations.

Contribution

It provides a comprehensive classification of BPS equations and supersymmetry fractions in 6D and 8D pure Yang-Mills theories, including explicit solutions.

Findings

Identified all possible supersymmetry fractions preserved by BPS states.

Derived self-dual BPS equations for six and eight dimensions.

Applied results to explicit finite and infinite energy configurations on various spaces.

Abstract

We consider the maximal supersymmetric pure Yang-Mills theories on six and eight dimensional space. We determine, in a systematic way, all the possible fractions of supersymmetry preserved by the BPS states and present the corresponding `self-dual' BPS equations. In six dimensions the intrinsic one has 1/4 supersymmetry, while in eight dimensions, 1/16, 2/16, ..., 6/16. We apply our results to some explicit BPS configurations of finite or infinite energy on commutative or noncommutative spaces.