Sasakian quiver gauge theories and instantons on Calabi-Yau cones

Olaf Lechtenfeld, Alexander D. Popov, Richard Joseph Szabo

Research output: Contribution to journalArticle

3 Citations (Scopus)
46 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)821-882
Number of pages62
JournalAdvances in Theoretical and Mathematical Physics
Volume20
Issue number4
DOIs
Publication statusPublished - 4 Nov 2016

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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