Interactions of Domain Walls of SUSY Yang-Mills as D-Branes

TL;DR

This paper explores the dynamics of supersymmetric Yang-Mills domain walls, modeling them as D-branes and analyzing their interactions through a 2+1D gauge theory, revealing agreement with exact tension formulas.

Contribution

It extends the open string description of domain wall interactions to multiple walls, capturing their qualitative force behavior at leading order in 1/N.

Findings

The potential admits a supersymmetric bound state when all walls are coincident.

The force behavior matches the exact tension formula at large separations.

The model accurately describes interactions for an arbitrary number of walls.

Abstract

Domain walls in supersymmetric Yang-Mills are BPS configurations which preserve two supercharges of the parent theory and so their tensions are known exactly. On the other hand, they have been described as D-branes for the confining string. This leads to a description of their collective dynamics in terms of a 2+1 -dimensional gauge theory with two supersymmetries and a Chern-Simons term. We show that this open string description can capture the qualitative behaviour of the forces between the domain walls for an arbitrary configuration of n walls at leading order in 1/N, extending earlier calculations for two walls. The potential admits a supersymmetric bound state when the n walls are all coincident and asymptotes to a constant at large separation with an n dependence which agrees perfectly with the exact tension formula.