New Einstein-Sasaki Spaces in Five and Higher Dimensions

We obtain infinite classes of new Einstein-Sasaki metrics on complete and nonsingular manifolds. They arise, after Euclideanization, 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 $U(1)\times U(1)\times U(1)$ isometry group. They are topologically $S^2\times S^3$. Their AdS/CFT duals describe quiver theories on the four-dimensional boundary of ${\mathrm{AdS}}_5$. 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.