Sitting on the Domain Walls of N=1 Super Yang-Mills

TL;DR

This paper explores the properties of domain walls in N=1 super Yang-Mills theory, modeling them as D-branes and analyzing their interactions through a 2+1D gauge theory, revealing insights into their bound states and potential energies.

Contribution

It provides a detailed analysis of the world-volume gauge theory of domain walls, including two-loop potential calculations and estimates of bound state sizes, advancing understanding of their non-perturbative dynamics.

Findings

Two-loop quadratic potential supports supersymmetric bound states.

Mass gap of order Lambda/N around the minimum.

Potential at large distances accounts for binding energy.

Abstract

In pure N=1 supersymmetric Yang-Mills with gauge group SU(N), the domain walls which separate the N vacua have been argued, on the basis of string theory realizations, to be D-branes for the confining string. In a certain limit, this means that a configuration of k parallel domain walls is described by a 2+1-dimensional U(k) gauge theory. This theory has been identified by Acharya and Vafa as the U(k) gauge theory with 4 supercharges broken by a Chern-Simons term of level N in such a way that 2 supercharges are preserved. We argue further that the gauge coupling of the domain wall gauge theory goes like g^2 ~ Lambda/N, for large N. In the case of two domain walls, we show that the U(2) world-volume theory generates a quadratic potential on the Coulomb branch at two loops in perturbation theory which is consistent with there being a supersymmetric bound state of the two wall system. A mass gap of order Lambda/N is generated around the supersymmetric minimum and we estimate the size of the bound-state to be order Lambda/ \sqrt N. At large distance the potential reaches a constant that can qualitatively account for the binding energy of the two walls even though stringy effects are not, strictly speaking, decoupled.