Double quiver gauge theory and nearly Kahler flux compactifications

TL;DR

This paper explores the reduction of Yang-Mills theory on specific six-dimensional spaces with nearly Kahler structures, establishing a correspondence between certain vector bundles and quiver representations, and linking instanton solutions to vortex equations.

Contribution

It introduces a novel equivalence between G-equivariant pseudo-holomorphic bundles and quiver bundles on manifolds with nearly Kahler structures, including relations that prevent oriented cycles.

Findings

Equivalence between G-equivariant bundles and quiver bundles with relations.

Correspondence between Spin(7)-instantons and quiver vortex solutions.

Identification of non-trivial cycles in quivers for generic instanton configurations.

Abstract

We consider G-equivariant dimensional reduction of Yang-Mills theory with torsion on manifolds of the form MxG/H where M is a smooth manifold, and G/H is a compact six-dimensional homogeneous space provided with a never integrable almost complex structure and a family of SU(3)-structures which includes a nearly Kahler structure. We establish an equivalence between G-equivariant pseudo-holomorphic vector bundles on MxG/H and new quiver bundles on M associated to the double of a quiver Q, determined by the SU(3)-structure, with relations ensuring the absence of oriented cycles in Q. When M=R^2, we describe an equivalence between G-invariant solutions of Spin(7)-instanton equations on MxG/H and solutions of new quiver vortex equations on M. It is shown that generic invariant Spin(7)-instanton configurations correspond to quivers Q that contain non-trivial oriented cycles.