Moduli space dimensions of multipronged strings

The numbers of bosonic and fermionic zero modes of multipronged strings are counted in $\mathcal{N}=4\mathrm{}$ super-Yang-Mills theory and compared with those of the type IIB string theory. We obtain nice agreement for the fermionic zero modes, while our result for the bosonic zero modes differs from that obtained in the type IIB string theory. The possible origin of the discrepancy is discussed.