Walls and vortices in supersymmetric non-abelian gauge theories

TL;DR

This paper reviews recent advances in understanding BPS multi-wall solutions, vortices, and monopoles in five-dimensional supersymmetric non-Abelian gauge theories, highlighting exact solutions and the structure of their moduli spaces.

Contribution

It provides a comprehensive analysis of the moduli space of BPS solutions, including exact solutions at infinite gauge coupling and the characterization of 1/4 BPS solutions.

Findings

Moduli space of BPS non-Abelian walls is the complex Grassmann manifold.

Exact solutions are obtained for infinite gauge coupling.

Full moduli space of 1/4 BPS solutions is described by holomorphic maps.

Abstract

We review recent results on the BPS multi-wall solutions in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Total moduli space of the BPS non-Abelian walls is found to be the complex Grassmann manifold SU(N_F)/[SU(N_C)xSU(N_F-N_C)xU(1)]. Exact solutions are obtained with full generic moduli for infinite gauge coupling. A 1/4 BPS equation is also solved, giving vortices together with the non-Abelian walls and monopoles in the Higgs phase attached to the vortices. The full moduli space of the 1/4 BPS solutions is found to be holomorphic maps from a complex plane to the wall moduli space.