Counting Yang-Mills dyons with index theorems - art. no. 125006

We count the supersymmetric bound states of many distinct BPS monopoles in N=4 Yang-Mills theories and in pure N=2 Yang-Mills theories. The novelty he re is that we work in generic Coulombic vacua where more than one adjoint H iggs fields are turned on. The number of purely magnetic bound states is ag ain found to be consistent with the electromagnetic duality of the N=4 SU(n ) theory, as expected. We also count dyons of generic electric charges, whi ch correspond to 1/4 BPS dyons in N=4 theories and 1/2 BPS dyons in N = 2 t heories. Surprisingly, the degeneracy of dyons is typically much larger tha n would be accounted for by a single supermultiplet of appropriate angular momentum, implying many supermultiplets of the same charge and the same mas s.