We obtain infinite classes of new Einstein-Sasaki metrics on complete and non-singular manifolds. They arise, after Euclideanisation, from BPS limits of the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces L^{p,q,r} in five dimensions have cohomogeneity 2, and U(1) x U(1) x U(1) isometry group. They are topologically S^2 x S^3. Their AdS/CFT duals will describe quiver theories on the four-dimensional boundary of AdS_5. We also obtain new Einstein-Sasaki spaces of cohomogeneity n in all odd dimensions D=2n+1 \ge 5, with U(1)^{n+1} isometry.

Revtex, 4 pages, metric regularity conditions are further refined