SU(3)-Instantons and G2,Spin(7)-Heterotic String Solitons

Necessary and sufficient conditions to the existence of a hermitian connection with totally skew-symmetric torsion and holonomy contained in SU(3) are given. A formula for the Riemannian scalar curvature is obtained. Non-compact solution to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton is found in dimension 6. Non-conformally flat non-compact solutions to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton are found in dimensions 7 and 8. A Riemannian metric with holonomy contained in G2 arises from our considerations and Hitchin’s flow equations, which seems to be new. Compact examples of SU(3),G2 and Spin(7) instanton satisfying the anomaly cancellation conditions are presented.