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

TL;DR

This paper explores the AdS/CFT correspondence involving seven-dimensional inhomogeneous Sasaki-Einstein manifolds, using particle approximations and scalar Laplace solutions to connect supergravity spectra with dual conformal field theories.

Contribution

It establishes a concrete mapping between conserved quantities and eigenmodes on $Y^{p,k}$ manifolds, advancing understanding of their dual field theories.

Findings

Geodesic motion analysis for conserved quantities

Scalar Laplace eigenmodes match Kaluza-Klein spectrum

Dual operators identified in conformal field theory

Abstract

Seven-dimensional inhomogeneous Sasaki-Einstein manifolds $Y^{p,k}(KE_4)$ present a challenging example of AdS/CFT correspondence. At present, their field theory duals for $KE_4=\mathbb{CP}^2$ base are proposed only within a restricted range $3p/2\le k \le 2p$ as ${\cal N}=2$ 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 ${\rm AdS}_4\times Y^{p,k}$, and are dual to protected operators written in terms of matter multiplets in the dual conformal field theory.