1009.3208 (Alexander D. Popov et al.)

Double quiver gauge theory and nearly Kahler flux compactifications    [PDF]

Alexander D. Popov, Richard J. Szabo

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.

View original: http://arxiv.org/abs/1009.3208