7-DIMENSIONAL OCTONIONIC YANG-MILLS INSTANTON AND ITS EXTENSION TO ANHETEROTIC STRING SOLITON

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 octo nionic instanton has an extension to a solitonic solution of the low e nergy effective theory of the heterotic string that preserves two of t he sixteen supersymmetries and hence corresponds to N = 1 space-time s upersymmetry in (2 + 1) dimensions transverse to the seven dimensions where the Yang-Mills instanton is defined.