Interactions of domain walls of SUSY Yang-Mills as D-branes

Domain walls in supersymmetric Yang-Mills are BPS configurations whichpreserve two supercharges of the parent theory and so their tensions are knownexactly. On the other hand, they have been described as D-branes for theconfining string. This leads to a description of their collective dynamics interms of a 2+1 -dimensional gauge theory with two supersymmetries and aChern-Simons term. We show that this open string description can capture thequalitative behaviour of the forces between the domain walls for an arbitraryconfiguration of n walls at leading order in 1/N, extending earliercalculations for two walls. The potential admits a supersymmetric bound statewhen the n walls are all coincident and asymptotes to a constant at largeseparation with an n dependence which agrees perfectly with the exact tensionformula.