Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals
type: Item
instance of: scholarly article
title: Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals
zbMATH Open document ID: 1112.53034
author: Dario Martelli
author: James Sparks
published in: Communications in Mathematical Physics
publication date: 2006-11-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/0411238
review text: The authors consider an infinite family of Sasaki-Einstein metrics \(Y^{p,q}\) on \(S^2 \times S^3\), where \(p\) and \(q\) are coprime positive integers and \(q < p\). A family of toric Calabi-Yau cones is associated to it, which are shown to be Kähler quotients \({\mathbb C}^4 /U(1)\) (the vacua of gauged linear sigma models, generalizing the conifold). It is proved that the corresponding toric diagrams may be embedded in that of the orbifold \({\mathbb C}^3 / {\mathbb Z}_{p+1} \times {\mathbb Z}_{p+1}\). It follows that the \(Y^{p,q}\) manifolds are AdS/CFT dual to an infinite class of superconformal field theories. As a particular application, it is shown that \(Y^{2,1}\) is an irregular Sasaki-Einstein metric on the horizon of the complex cone over the first del Pezzo surface; the exact central charge at its \(\mathbb{R}\) fixed point, predicted for this theory, is a quadratic irrational number and agrees with an independent recent purely field theoretic calculation. The paper contains also some reviews on Sasaki-Einstein geometry, symplectic toric geometry and the moment map.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 5076580
zbMATH Keywords: Sasaki-Einstein metrics
zbMATH Keywords: Calabi-Yau cones
zbMATH Keywords: toric geometry
zbMATH Keywords: AdS/CFT duality
zbMATH Keywords: gauge theory
reviewed by: Gabriel Teodor Pripoae
MaRDI profile type: Publication
OpenAlex ID: W3101636200
arXiv ID: hep-th/0411238
cites work: The large \(N\) limit of superconformal field theories and supergravity
cites work: Superconformal field theory on threebranes at a Calabi-Yau singularity
cites work: Non-spherical horizons. I
cites work: Sasaki-Einstein metrics on \(S^2\times S^3\)
cites work: Supersymmetric AdS 5 solutions of M-theory
cites work: On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay
cites work: The exact superconformal \(R\)-symmetry maximizes \(a\)
cites work: D-brane gauge theories from toric singularities and toric duality
cites work: A new infinite class of Sasaki-Einstein manifolds
cites work: Q5311073
cites work: A note on Einstein–Sasaki metrics in D ⩾ 7
cites work: On Kähler-Einstein metrics on certain Kähler manifolds with \(C_ 1(M)>0\)
cites work: Kähler-Einstein metrics on complex surfaces with \(C_ 1>0\)
cites work: Contact toric manifolds
cites work: Phases of \(N=2\) theories in two dimensions
cites work: D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds
cites work: On the structure of 5-manifolds
cites work: Einstein manifolds of dimension five with small first eigenvalue of the Dirac operator
cites work: Sur la Structure du Groupe d’Homéomorphismes Analytiques d’une Certaine Variété Kaehlérinne
cites work: On the geometry of Sasakian-Einstein 5-manifolds
cites work: Sasakian-Einstein structures on $9\#(S^2\times S^3)$
cites work: New Einstein metrics on \(8\#(S^{2}\times S^{3})\).
cites work: Einstein metrics on principal torus bundles
cites work: Moment maps on symplectic cones
cites work: Convexity and Commuting Hamiltonians
cites work: Convexity properties of the moment mapping
cites work: Hamiltonian torus actions on symplectic orbifolds and toric varieties
cites work: A note on toric contact geometry
cites work: Homotopy groups of 𝐾-contact toric manifolds
cites work: \(\mathcal N=2\) conformal field theories from M2-branes at conifold singularities
cites work: 3D superconformal theories from Sasakian seven-manifolds: new non-trivial evidences for \(\text{AdS}_ 4/\text{CFT}_ 3\).
cites work: M-theory on the Stiefel manifold and 3d conformal field theories
cites work: Baryon charges in 4d superconformal field theories and their AdS duals
DOI: 10.1007/S00220-005-1425-3
description: scientific article