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Toric Geometry, Sasaki–Einstein Manifolds and a new Infinite Class of AdS/CFT duals
| Citations: | 173 - 15 self |
BibTeX
@MISC{Martelli_toricgeometry,,
author = {Dario Martelli and James Sparks},
title = {Toric Geometry, Sasaki–Einstein Manifolds and a new Infinite Class of AdS/CFT duals},
year = {}
}
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Abstract
Recently an infinite family of explicit Sasaki–Einstein metrics Y p,q on S 2 × S 3 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 Kähler quotients C 4 //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 C 3 /Zp+1 × Zp+1 for all q < p with fixed p. We hence find that the Y p,q manifolds are AdS/CFT dual to an infinite class of N = 1 superconformal field theories arising as infra–red (IR) fixed points of toric quiver gauge theories with gauge group SU(N) 2p. As a non–trivial example, we show that Y 2,1 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
Keyphrases
toric geometry new infinite class ad cft duals sasaki einstein manifold first del pezzo surface toric quiver gauge theory hler quotient corresponding family toric diagram explicit irregular sasaki einstein non trivial example calabi yau cone ad cft infinite class coprime positive integer dual quiver gauge theory complex cone superconformal field theory gauge group su explicit sasaki einstein metric corresponding toric diagram infinite family gauged linear sigma model several recent result
