Classification of BPS equations in higher dimensions

TL;DR

This paper provides a comprehensive classification of BPS equations across various dimensions, revealing their symmetries and connections with self-dual Yang-Mills equations, and explores applications in supersymmetric theories and string theory.

Contribution

It introduces a general method to derive BPS equations in any dimension and classifies all such equations in Euclidean and Minkowski spaces up to certain dimensions.

Findings

Classified all BPS equations in Euclidean dimensions up to 8.

Identified symmetries and connections with self-dual Yang-Mills equations.

Derived BPS equations in Minkowski space up to 6 dimensions.

Abstract

We systematically classify all possible Bogomol'nyi-Prasad-Sommerfield (BPS) equations in Euclidean dimension $d\leq8$. We discuss symmetries of BPS equations and their connection with the self-dual Yang-Mills equations. Also, we present a general method allowing to obtain the BPS equations in any dimension. In addition, we find all BPS equations in the Minkowski space of dimension $d\leq6$ and apply the obtained results to the supersymmetric Yang-Mills theories. In conclusion, we discuss the possibility of using the classification to construct soliton solutions of the low-energy effective theory of the heterotic string.