Moduli Space of BPS Walls in Supersymmetric Gauge Theories

TL;DR

This paper proves the existence and uniqueness of BPS domain wall solutions in supersymmetric gauge theories, establishing their moduli space as complex projective space and extending results to non-Abelian cases with bounds on moduli space dimensions.

Contribution

It provides a rigorous proof of the moduli space structure for BPS walls in supersymmetric gauge theories, including finite gauge couplings and non-Abelian extensions.

Findings

Moduli space of BPS walls is CP^(N_f-1) at finite gauge coupling.

Extension of proof to U(N_c) gauge theories with U(1)-factorizable moduli matrix.

Derived sharp estimates for exponential decay depending on gauge coupling and mass differences.

Abstract

Existence and uniqueness of the solution are proved for the `master equation' derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with Nf charged matter hypermultiplets with eight supercharges. This proof finally establishes the fact that the moduli space of the BPS domain wall solution is CP^(N_f-1) for the gauge theory at finite gauge couplings. Therefore the moduli space at finite gauge couplings is topologically the same manifold as that at infinite gauge coupling, where the gauged linear sigma model reduces to a nonlinear sigma model. The proof is extended to the U(Nc) gauge theory with Nf hypermultiplets in the fundamental representation, provided the moduli matrix of the domain wall solution is U(1)-factorizable. Thus the dimension of the moduli space of U(Nc) gauge theory is bounded from below by the dimension of the U(1)-factorizable part of the moduli space. We also obtain sharp estimates of the asymptotic exponential decay which depend on both the gauge coupling and the hypermultiplet mass differences.