Fermions in Bosonic String Theories

TL;DR

This paper demonstrates the fermionic nature of certain bound states involving instantons in bosonic string theories, expanding the understanding of fermion emergence in purely bosonic frameworks through topological and conformal field theory analyses.

Contribution

It generalizes the Jackiw-Rebbi-Hasenfratz-'t Hooft construction to show fermions arise from bosonic string configurations, identifying new fermionic excitations in various string theories.

Findings

Identified fermionic excitations in type 0B and 0A string theories.

Confirmed fermionic nature through conformal field theory analysis.

Revealed a spectrum of fermions in bosonic string compactifications.

Abstract

We generalize the Jackiw-Rebbi-Hasenfratz-'t Hooft construction of fermions from bosons to demonstrate the fermionic nature of certain bound states involving SU(N) instantons in even spatial dimensions and SO(N) instantons in $8k+1$ spatial dimensions. We use this result to identify several fermionic excitations in various perturbatively bosonic string theories. In some examples we are able to identify these fermions as excitations in known conformal field theories and independently confirm their fermionic nature. Examples of the fermions we find include certain 3-string junctions in type 0B theory, excitations of the 0-p system in type 0A theory, excitations of the stable D-particle of type O theory, and a rich spectrum of fermions in the bosonic string compactified on the SO(32) group lattice.