TY - JOUR

T1 - Sasakian quiver gauge theories and instantons on Calabi-Yau cones

AU - Lechtenfeld, Olaf

AU - Popov, Alexander D.

AU - Szabo, Richard J.

N1 - Funding Information: The work of OL and ADP was partially supported by the Deutsche Forschungsgemeinschaft under Grant LE 838/13. The work of RJS was partially supported by the Consolidated Grant ST/L000334/1 from the UK Science and Technology Facilities Council. This work was completed while RJS was visiting the Hausdorff Research Institute for Mathematics in Bonn during the 2014 Trimester Program "Noncommutative Geometry and its Applications"; he would like to thank Alan Carey, Victor Gayral, Matthias Lesch, Walter van Suijlekom and Raimar Wulkenhaar for the invitation, and all the staff at HIM for the warm hospitality. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84995495859&partnerID=8YFLogxK

U2 - 10.4310/ATMP.2016.v20.n4.a4

DO - 10.4310/ATMP.2016.v20.n4.a4

M3 - Article

AN - SCOPUS:84995495859

VL - 20

SP - 821

EP - 882

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

SN - 1095-0761

IS - 4

ER -