Non-toric Cones and Chern-Simons Quivers

Abstract

We obtain an integral formula for the volume of non-toric tri-Sasaki Einstein manifolds arising from nonabelian hyperkahler quotients. The derivation is based on equivariant localization and generalizes existing formulas for Abelian quotients, which lead to toric manifolds. The formula is particularly valuable in the context of AdS${}_4\times Y_7$ vacua of M-theory and their field theory duals. As an application, we consider 3d $\mathcal{N}=3$ Chern-Simons theories with affine ADE quivers. While the $\hat{A}$ series corresponds to toric $Y_7$, the $\hat{D}$ and $\hat{E}$ series are non-toric. We compute the volumes of the corresponding seven-manifolds and compare to the prediction from supersymmetric localization in field theory, finding perfect agreement. This is the first test of an infinite number of non-toric AdS${}_4$/CFT${}_3$ dualities.

2+24 pages. v2: Minor improvements to the text. Matches published version

References in corpus (5)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Sasaki-Einstein Manifolds and Volume Minimisation
• Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
• Sasaki-Einstein Metrics on S^2 x S^3
• AdS/CFT with Tri-Sasakian Manifolds

Cited by in corpus (8)

• A Universal Counting of Black Hole Microstates in AdS${}_4$
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• Strong Coupling Limit of A Family of Chern-Simons-matter Theories
• Charges of Monopole Operators in $\widehat{ADE}$ Chern-Simons Quiver Gauge Theories
• Classical Monopole Solutions to $\mathcal{N}=3$ Chern-Simons-Yang-Mills Theories
• Superconformal Index for $\mathcal{N}=3$ $\widehat{ADE}$ Chern-Simons Quiver Gauge Theories