1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --

TL;DR

This paper classifies various BPS equations in supersymmetric gauge theories across multiple dimensions, revealing new equations and rederiving known ones, thereby advancing understanding of supersymmetric solitons and brane configurations.

Contribution

It provides a comprehensive classification of 1/2, 1/4, and 1/8 BPS equations in SUSY gauge theories with arbitrary gauge groups and matter, including new equations in lower dimensions.

Findings

Identifies unique 1/8 BPS equations in six dimensions.

Derives all known BPS equations and discovers new ones in lower dimensions.

Clarifies the structure of BPS solitons and their relation to brane configurations.

Abstract

We systematically classify 1/2, 1/4 and 1/8 BPS equations in SUSY gauge theories in d=6, 5, 4, 3 and 2 with eight supercharges, with gauge groups and matter contents being arbitrary. Instantons (strings) and vortices (3-branes) are only allowed 1/2 BPS solitons in d=6 with N=1 SUSY. We find two 1/4 BPS equations and the unique 1/8 BPS equation in d=6 by considering configurations made of these field theory branes. All known BPS equations are rederived while several new 1/4 and 1/8 BPS equations are found in dimension less than six by dimensional reductions.