SU(3)-instantons and $G_2, Spin(7)$-heterotic string solitons

Details SU(3)-instantons and $G_2, Spin(7)$-heterotic string solitons SU(3)-instantons and $G_2, Spin(7)$-heterotic string solitons

2003-12-03

arxiv.org/abs/math/0312094v6

Commun.Math.Phys. 259 (2005) 79-102

Mathematics

Differential Geometry

LaTex, 22 pages, Corrected anomaly cancellation, final version to appear in Commun. Math. Phys

Scientific paper

10.1007/s00220-005-1396-4

Necessary and sufficient conditions to the existence of a hermitian connection with totally skew-symmetric torsion and holonomy contained in SU(3) are given. Non-compact solution to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton is found in dimensions 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 $G_2$ arises from our considerations and Hitchin's flow equations, which seems to be new. Compact examples of $SU(3), G_2$ and $Spin(7)$ instanton satisfying the anomaly cancellation conditions are presented.

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