Fermionic zero-modes around string solitons

In the presence of string solitons, index theorems for the generalised Dirac operators have to be revisited. We show that in supersymmetric configurations the fermionic operators decouple, so that there are no mixing effects between different fermions in the index theorems. We extend the index theorems in the presence of torsion to the generic case of manifolds with boundary, which naturally appear in string solutions, and apply this result to the soliton solution of Callan, Harvey and Strominger.