Multi-instantons in higher dimensions and superstring solitons
We construct an octonionic multi-instantons to the seven dimentional 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 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) dimentions transverse to the seven dimensions where the Yang-Mills instanton is defined. Moreover, we prove that this $7D$ instanton solution is $E_6$-invariant and may be easy to extend in eight dimentions. An extended-soliton solution to the low-energy heterotic-field-theory equations of motion is constructed from this eight-dimentional octonionic multi-instanton. The soliton describes a string in ten-dimentional Minkowski space, and preserves only one of the sixteen spacetime supersymmetries.