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.

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References in corpus (10)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• On the moduli space of elliptic Maxwell-Chern-Simons theories
• Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
• M2-branes on Orbifolds of the Cone over Q^{1,1,1}
• Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories
• On the multi-spin magnon and spike solutions from membranes
• Toward NS5 Branes on the Resolved Cone over Y^{p,q}
• Rotating Membranes in AdS_4xM^{1,1,1}
• Integrable systems from membranes on AdS_4 x S^7