A Note on Domain Walls and the Parameter Space of N=1 Gauge Theories

TL;DR

This paper investigates the spectrum and stability of BPS domain walls in N=1 U(N) gauge theories with adjoint matter, revealing discontinuities and singularities linked to the matrix model description of vacua.

Contribution

It provides a detailed analysis of BPS domain wall multiplicities and their discontinuities across marginal stability curves in the parameter space of N=1 gauge theories.

Findings

Discontinuities in BPS wall multiplicities occur on marginal stability curves.

The structure of these curves is connected to singularities in the matrix model.

Large N behavior reveals a link between stability curves and matrix model singularities.

Abstract

We study the spectrum of BPS domain walls within the parameter space of N=1 U(N) gauge theories with adjoint matter and a cubic superpotential. Using a low energy description obtained by compactifying the theory on R^3 x S^1, we examine the wall spectrum by combining direct calculations at special points in the parameter space with insight drawn from the leading order potential between minimal walls, i.e those interpolating between adjacent vacua. We show that the multiplicity of composite BPS walls -- as characterised by the CFIV index -- exhibits discontinuities on marginal stability curves within the parameter space of the maximally confining branch. The structure of these marginal stability curves for large N appears tied to certain singularities within the matrix model description of the confining vacua.