BPS pion domain walls in the supersymmetric chiral Lagrangian

TL;DR

This paper constructs exact BPS pion domain wall solutions in a supersymmetric SU(N) chiral Lagrangian with various superpotentials, revealing new vacua and the preservation of half supersymmetry, but not connecting all vacua via domain walls.

Contribution

It provides explicit BPS domain wall solutions in a supersymmetric chiral Lagrangian with novel vacua and explores their supersymmetry properties and limitations.

Findings

Domain walls preserve half of supersymmetry.

Not all vacua are connected by BPS domain walls.

New vacua appear with quadratic superpotential.

Abstract

We construct exact solutions of BPS pion domain walls in the four-dimensional $\mathcal{N}=1$ supersymmetric SU(N) chiral Lagrangian with pion masses introduced via linear and quadratic superpotentials. The model admits N discrete vacua in the center of SU(N) for the linear superpotential. In addition to the latter, new vacua appear for the quadratic superpotential. We find that the domain wall solutions of pions (Nambu-Goldstone bosons) that interpolate between a pair of (pion) vacua preserve half of supersymmetry. Contrary to our expectations, we have not been able to find domain walls involving the quasi-Nambu-Goldstone bosons present in the theory, which in turn has the consequence that not all vacua of the theory are connected by a BPS domain wall solution.