2004/11/30 by Dario Martelli, James Sparks · 3 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Dual polyhedron #Fixed point #Gauge theory #Geometry and complex manifolds #Metric (unit) #Moduli space #Orbifold #Quiver #Quotient #Superpotential #Toric variety #hep-th #math.DG
paper · pdf · doi:10.1007/s00220-005-1425-3
published as Commun.Math.Phys. 262 (2006) 51-89 · 54 pages, 5 figures; minor changes; further minor changes, ref [8] added - published version; eqns 1.3, 1.4 removed
openalex publication_date 2005/11/23 · arxiv created 2006/08/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Recently an infinite family of explicit Sasaki-Einstein metrics Yp,q on S2 x S3 has been discovered, where p and q are two coprime positive integers, with q<p. These give rise to a corresponding family of Calabi-Yau cones, which moreover are toric. Aided by several recent results in toric geometry, we show that these are Kahler quotients C4//U(1), namely the vacua of gauged linear sigma models with charges (p,p,-p+q,-p-q), thereby generalising the conifold, which is p=1,q=0. We present the corresponding toric diagrams and show that these may be embedded in the toric diagram for the orbifold C3/Zp+1xZp+1 for all q<p with fixed p. We hence find that the Yp,q manifolds are AdS/CFT dual to an infinite class of N=1 superconformal field theories arising as IR fixed points of toric quiver gauge theories with gauge group SU(N)2p. As a non-trivial example, we show that Y2,1 is an explicit irregular Sasaki-Einstein metric on the horizon of the complex cone over the first del Pezzo surface. The dual quiver gauge theory has already been constructed for this case and hence we can predict the exact central charge of this theory at its IR fixed point using the AdS/CFT correspondence. The value we obtain is a quadratic irrational number and, remarkably, agrees with a recent purely field theoretic calculation using a-maximisation.