Sasakian quiver gauge theories and instantons on Calabi-Yau cones

authored by

Olaf Lechtenfeld, Alexander D. Popov, Richard J. Szabo

Abstract

We consider SU(2)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form M × S³/G, where M is a smooth manifold and S³/G is a three-dimensional Sasaki-Einstein orbifold. We obtain new quiver gauge theories on M whose quiver bundles are based on the affine ADE Dynkin diagram associated to G. We relate them to those arising through translationally-invariant dimensional reduction over the associated Calabi-Yau cones C(S³/G) which are based on McKay quivers and ADHM matrix models, and to those arising through SU(2)-equivariant dimensional reduction over the leaf spaces of the characteristic foliations of S³/G which are Kähler orbifolds of ℂP1 whose quiver bundles are based on the unextended Dynkin diagram corresponding to G. We use Nahm equations to describe the vacua of SU(2)-equivariant quiver gauge theories on the cones as moduli spaces of spherically symmetric instantons. We relate them to the Nakajima quiver varieties which can be realized as Higgs branches of the worldvolume quiver gauge theories on Dp-branes probing D(p + 4)-branes which wrap an ALE space, and to the moduli spaces of spherically symmetric solutions in putative non-abelian generalizations of two-dimensional affine Toda field theories.

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics

External Organisation(s)

Heriot-Watt University
Maxwell Institute for Mathematical Sciences
University of Edinburgh

Type

Artikel

Journal

Advances in Theoretical and Mathematical Physics

Volume

20

Pages

821-882

No. of pages

62

ISSN

1095-0761

Publication date

2016

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Mathematik (insg.), Physik und Astronomie (insg.)

Electronic version(s)

https://doi.org/10.4310/ATMP.2016.v20.n4.a4 (Access: Unbekannt)