Complete factorization of equations of motion in supersymmetric field theories

TL;DR

This paper demonstrates how to factorize equations of motion in supersymmetric field theories into first-order Bogomol'nyi equations, enabling explicit analysis of topological defects with Z_N symmetry.

Contribution

It provides a complete factorization method for equations of motion in supersymmetric theories with scalar fields, revealing all topological sectors and their integrability.

Findings

All topological defects are of BPS type.

Explicit models with Z_N symmetry are analyzed.

The equations of motion are fully factorized into first-order equations.

Abstract

We investigate bosonic sectors of supersymmetric field theories. We consider superpotentials described by one and by two real scalar fields, and we show how the equations of motion can be factorized into a family of first order Bogomol'nyi equations, so that all the topological defects are of the Bogomol'nyi-Prasad-Sommerfield type. We examine explicit models, that engender the Z_N symmetry, and we identify all the topological sectors, illustrating their integrability.