Non-Abelian Walls in Supersymmetric Gauge Theories

TL;DR

This paper constructs exact multi-wall solutions in five-dimensional supersymmetric U(N_C) gauge theories, revealing the structure of their moduli space and effective world-volume theories, including non-Abelian features.

Contribution

It provides explicit BPS multi-wall solutions with full moduli in supersymmetric gauge theories, including the complete moduli space and effective world-volume theories.

Findings

Exact multi-wall solutions with full moduli are obtained.

The total moduli space is identified as a complex Grassmann manifold.

Effective theories for the moduli fields are constructed and analyzed.

Abstract

The Bogomol'nyi-Prasad-Sommerfield (BPS) multi-wall solutions are constructed in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Exact solutions are obtained with full generic moduli for infinite gauge coupling and with partial moduli for finite gauge coupling. The generic wall solutions require nontrivial configurations for either gauge fields or off-diagonal components of adjoint scalars depending on the gauge. Effective theories of moduli fields are constructed as world-volume gauge theories. Nambu-Goldstone and quasi-Nambu-Goldstone scalars are distinguished and worked out. Total moduli space of the BPS non-Abelian walls including all topological sectors is found to be the complex Grassmann manifold SU(N_F) / [SU(N_C) x SU(N_F-N_C) x U(1)] endowed with a deformed metric.