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

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.

33 pages, LaTeX, 6 eps figures; v2: references added

References in corpus (10)

• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• On Geometry and Matrix Models
• Phases of N=1 Supersymmetric Gauge Theories and Matrices
• Domain Walls and Flux Tubes in N=2 SQCD: D-Brane Prototypes
• Chiral Rings and Phases of Supersymmetric Gauge Theories
• Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
• Exact Superpotentials from Matrix Models
• Quantum parameter space in super Yang-Mills, II
• N=1 G_2 SYM theory and Compactification to Three Dimensions
• On Effective Superpotentials and Compactification to Three Dimensions

Cited by in corpus (9)

• Manifestly Supersymmetric Effective Lagrangians on BPS Solitons
• D-brane Construction for Non-Abelian Walls
• Webs of Walls
• Global Structure of Moduli Space for BPS Walls
• Duality and Modularity in Elliptic Integrable Systems and Vacua of N=1* Gauge Theories
• Permutations of Massive Vacua
• Hidden Modulus in the Extended Veneziano-Yankielowicz Theory
• Two types of domain walls in $\mathcal{N}=1$ super-QCD: how they are classified and counted
• Domain walls in super Yang-Mills: worldvolume TQFTs and deconfinement from semiclassics on ${\mathbb{R}}^3\times {\mathbb{S}}^1$