Fermionic zero-modes around string solitons

TL;DR

This paper revisits index theorems for fermionic operators in string soliton backgrounds, showing decoupling in supersymmetric cases and extending theorems to manifolds with boundary, with applications to known string solutions.

Contribution

It extends index theorems to include torsion and boundary effects in supersymmetric string soliton contexts, clarifying fermionic zero-mode behavior.

Findings

Fermionic operators decouple in supersymmetric configurations

Index theorems extended to manifolds with boundary and torsion

Application to Callan-Harvey-Strominger string soliton solution

Abstract

In 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 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 by Callan, Harvey and Strominger.