M-theory and Seven-Dimensional Inhomogeneous Sasaki-Einstein Manifolds

Abstract

Seven-dimensional inhomogeneous Sasaki-Einstein manifolds $Y^{p,k}(K{E}_4)$ present a challenging example of AdS/CFT correspondence. At present, their field theory duals for $K{E}_4={\mathbb{CP}}^2$ base are proposed only within a restricted range $3p/2\le k\le 2p$ as $\mathcal{N}=2$ quiver Chern-Simons-matter theories with $SU(N)\times SU(N)\times SU(N)$ gauge group, nine bifundamental chiral multiplets interacting through a cubic superpotential. To further elucidate this correspondence, we use particle approximation both at classical and quantum level. We setup a concrete AdS/CFT mapping of conserved quantities using geodesic motions, and turn to solutions of scalar Laplace equation in $Y^{p,k}$. The eigenmodes also provide an interesting subset of Kaluza-Klein spectrum for $D=11$ supergravity in ${\mathrm{AdS}}_4\times Y^{p,k}$, and are dual to protected operators written in terms of matter multiplets in the dual conformal field theory.

v2 refs added. 19 pages 1 figure

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