Seven-dimensional octonionic Yang-Mills instanton and its extension to an heterotic string soliton

We construct an octonionic instanton solution to the seven-dimensional Yang-Mills theory based on the exceptional gauge group G₂ which is the automorphism group of the division algebra of octonions. This octonionic has an extension to a solitonic 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 (2+1) dimensions transverse to the seven dimensions where the Yang-Mills instanton is defined.