Physics Department,

Ivanovo State University,

39 Ermaka Str.,

Ivanovo 153025,

RUSSIA

E-mail: loginov@ivanovo.ac.ru

**Multi-instantons in higher dimensions and superstring
solitons**

**Abstract:**

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.