Sasakian quiver gauge theories and instantons on the conifold
Jakob C. Geipel, Olaf Lechtenfeld, Alexander D. Popov, Richard J. Szabo
Abstract
We consider Spin(4)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form
M
d
×
T
1,1
, where
M
d
is a smooth manifold and
T
1,1
is a five-dimensional Sasaki-Einstein manifold Spin(4)/U(1). We obtain new quiver gauge theories on
M
d
extending those induced via reduction over the leaf spaces
C
P
1
×C
P
1
in
T
1,1
. We describe the Higgs branches of these quiver gauge theories as moduli spaces of Spin(4)-equivariant instantons on the conifold which is realized as the metric cone over
T
1,1
. We give an explicit construction of these moduli spaces as Kähler quotients.