Self-intersection number of BPS junctions in backgrounds of three and seven-branes

In a recent paper De Wolfe et al. have shown how to use the self-intersecti on number of junctions to constrain the BPS spectrum of N = 2, D = 4 theori es with ADE flavor symmetry arising on a single D3-brane probe in a 7-brane background. Motivated by the existence of more general N = 2,D = 4 theorie s arising on the worldvolume of multiple D3-brane probes we show how to com pute the self-intersection number of junctions in the presence of 7-branes and multiple D3-branes.