All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation

TL;DR

This paper exactly solves a complex 1/4 BPS equation in supersymmetric gauge theories, revealing all configurations of walls, vortices, and monopoles, and characterizing their moduli space.

Contribution

It provides the complete set of solutions for a 1/4 BPS equation in supersymmetric gauge theories, including the structure of the moduli space of composite solitons.

Findings

All solutions of the 1/4 BPS equation are obtained explicitly.

The moduli space is characterized as the space of holomorphic maps to a deformed Grassmannian.

Monopoles in the Higgs phase are identified in U(1) gauge theory.

Abstract

We obtain all possible solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield equation exactly, containing configurations made of walls, vortices and monopoles in the Higgs phase. We use supersymmetric U(N_C) gauge theories with eight supercharges with N_F fundamental hypermultiplets in the strong coupling limit. The moduli space for the composite solitons is found to be the space of all holomorphic maps from a complex plane to the wall moduli space found recently, the deformed complex Grassmann manifold. Monopoles in the Higgs phase are also found in U(1) gauge theory.