Index Theorem for non-Supersymmetric Fermions Coupled to a non-Abelian String and Electric Charge Quantization

TL;DR

This paper derives electric charge quantization conditions and index theorems for non-supersymmetric fermions in non-Abelian string backgrounds, revealing a non-trivial dependence on the gauge group parameter N.

Contribution

It provides the first derivation of charge quantization and fermion zero mode index theorems for non-supersymmetric non-Abelian strings with detailed N dependence.

Findings

Charge quantization conditions for fermions in non-Abelian strings.

Index theorems for fermion zero modes with N dependence.

Non-trivial N dependence in both left-handed and right-handed fermion cases.

Abstract

Non-Abelian strings are considered in {\em non}-supersymmetric theories with fermions in various appropriate representations of the gauge group U($N$). We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases, we observe a non-trivial $N$ dependence.