Domain Walls Zoo in Supersymmetric QCD

TL;DR

This paper numerically explores complex domain wall solutions in supersymmetric QCD with SU(2), revealing various BPS and non-BPS walls, their existence ranges, and how they vanish or transform with changing matter field mass.

Contribution

It provides the first detailed numerical analysis of domain wall solutions, including BPS and sphaleron types, in supersymmetric QCD with varying matter field masses.

Findings

BPS domain walls exist for matter mass m < m* ≈ 4.67.

Sphaleron branches appear as saddle points in the energy landscape.

Complex walls disappear for m > m*, leaving only symmetric vacua connections.

Abstract

Solving numerically the equations of motion for the effective lagrangian describing supersymmetric QCD with the SU(2) gauge group, we find a menagerie of complex domain wall solutions connecting different chirally asymmetric vacua. Some of these solutions are BPS saturated walls; they exist when the mass of the matter fields does not exceed some critical value m < m* < 4.67059... There are also sphaleron branches (saddle points of the ebergy functional). In the range m* < m < m** \approx 4.83, one of these branches becomes a local minimum (which is not a BPS saturated one). At m > m*, the complex walls disappear altogether and only the walls connecting a chirally asymmetric vacuum with the chirally symmetric one survive.