Domain Walls in the Large N Limit

TL;DR

This paper investigates the structure of BPS domain walls in supersymmetric SU(N) Yang-Mills theories at large N, revealing a five-layer configuration with distinct phases through numerical analysis.

Contribution

It extends the understanding of domain wall structures to large N SU(N) theories, providing a detailed numerical profile in the Seiberg-Witten regime.

Findings

Five-layer structure of domain walls identified

Confinement and Coulomb phases separated by transition regions

Numerical minimization confirms the layered profile

Abstract

We study BPS saturated domain walls in supersymmetric SU(N) Yang-Mills theories in the large N limit. We focus on the Seiberg-Witten regime of ${\cal N}=2$ theory perturbed by a small mass ($m<O(\Lambda/N^4)$) and determine the wall profile by numerically minimizing its energy density. Similar to the SU(2) wall studied in a previous work, the SU(N) wall has a five layer structure, with two confinement phases on the outside, a Coulomb phase in the middle and two transition regions.