Sasakian quiver gauge theories and instantons on cones over round and squashed sevenspheres
Abstract
We study quiver gauge theories on the round and squashed sevenspheres, and orbifolds thereof. They arise by imposing $G$equivariance on the homogeneous space $G/H=\mathrm{SU}(4)/\mathrm{SU}(3)$ endowed with its SasakiEinstein structure, and $G/H=\mathrm{Sp}(2)/\mathrm{Sp}(1)$ as a 3Sasakian manifold. In both cases we describe the equivariance conditions and the resulting quivers. We further study the moduli spaces of instantons on the metric cones over these spaces by using the known description for Hermitian YangMills instantons on CalabiYau cones. It is shown that the moduli space of instantons on the hyperKahler cone can be described as the intersection of three Hermitian YangMills moduli spaces. We also study moduli spaces of translationally invariant instantons on the metric cone $\mathbb{R}^8/\mathbb{Z}_k$ over $S^7/\mathbb{Z}_k$.
 Publication:

arXiv eprints
 Pub Date:
 June 2017
 arXiv:
 arXiv:1706.07383
 Bibcode:
 2017arXiv170607383G
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Differential Geometry;
 Mathematics  Representation Theory;
 Mathematics  Symplectic Geometry
 EPrint:
 44 pages