An Index Theorem for Domain Walls in Supersymmetric Gauge Theories

The supersymmetric abelian Higgs model with N scalar fields admits multiple domain wall solutions. We perform a Callias-type index calculation to determine the number of zero modes of this soliton. We confirm that the most general domain wall has 2(N-1) zero modes, which can be interpreted as the positions and phases of (N-1) constituent domain walls. This implies the existence of moduli for a D-string interpolating between N D5-branes in IIB string theory.