Yang-Mills fields in flux compactifications on homogeneous manifolds with SU(4)-structure

摘要

The Spin(7)-instanton equations are natural BPS equations for instantons on 8-manifolds. We study these equations on nearly Kähler and Calabi-Yau torsion manifolds of the form M × G/H, with G/H a coset space and M a product of a torus with Euclidean space. By imposing G-invariance the instanton equations reduce to interesting equations on M ; for example, equations used by Kapustin and Witten in the geometric Langlands program arise in this way. We carry out reductions in a number of examples, and where possible present simple solutions.