Seven Dimensional Octonionic Yang-Mills Instanton and its Extension to an Heterotic String Soliton

TL;DR

This paper constructs a seven-dimensional octonionic Yang-Mills instanton based on the G2 gauge group and extends it to a heterotic string soliton, preserving minimal supersymmetry in a lower-dimensional effective theory.

Contribution

It introduces a novel octonionic instanton solution in seven dimensions and extends it to a heterotic string soliton with supersymmetry preservation.

Findings

Constructed a G2-based octonionic instanton in 7D.

Extended the instanton to a heterotic string soliton.

Preserves two of sixteen supersymmetries in the effective theory.

Abstract

We construct an octonionic instanton solution to the seven dimensional Yang-Mills theory based on the exceptional gauge group $G_2$ which is the automorphism group of the division algebra of octonions. This octonionic instanton has an extension to a solitonic two-brane solution of the low energy effective theory of the heterotic string that preserves two of the sixteen supersymmetries and hence corresponds to $N=1$ space-time supersymmetry in the (2+1) dimensions transverse to the seven dimensions where the Yang-Mills instanton is defined.