  Recently an infinite family of explicit Sasaki-Einstein metrics Y^{p,q} on
S^2 x 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 Kahler 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/Z_{p+1}xZ_{p+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 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 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.
