Scalar Laplacian on Sasaki-Einstein Manifolds Y^{p,q}

Abstract

We study the spectrum of the scalar Laplacian on the five-dimensional toric Sasaki-Einstein manifolds Y^{p,q}. The eigenvalue equation reduces to Heun's equation, which is a Fuchsian equation with four regular singularities. We show that the ground states, which are given by constant solutions of Heun's equation, are identified with BPS states corresponding to the chiral primary operators in the dual quiver gauge theories. The excited states correspond to non-trivial solutions of Heun's equation. It is shown that these reduce to polynomial solutions in the near BPS limit.

10 pages, references added

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• Holographic Systematics of D-brane Inflation
• Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• Index for Orbifold Quiver Gauge Theories
• Supersymmetric solutions for non-relativistic holography
• Supersymmetric Branes on AdS_5 x Y^{p,q} and their Field Theory Duals
• Brane Tilings and Exceptional Collections
• Toric Sasaki-Einstein manifolds and Heun equations
• A Note on Separability of Field Equations in Myers-Perry Spacetimes
• 1/N^2 corrections to the holographic Weyl anomaly
• Index for Supergravity on AdS_5 \times T^{1,1} and Conifold Gauge Theory
• Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial
• Sasakian Geometry, Holonomy, and Supersymmetry
• Baryonic branches and resolutions of Ricci-flat Kahler cones
• Scalar Field Contribution to Rotating Black Hole Entropy
• Kaluza-Klein Spectroscopy for the Leigh-Strassler SCFT
• Supersymmetric solutions based on Y^{p,q} and L^{p,q,r}
• The shortened KK spectrum of IIB supergravity on Y^{p,q}
• On the pp-wave limit and the BMN structure of new Sasaki-Einstein spaces
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• Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies
• M-theory and Seven-Dimensional Inhomogeneous Sasaki-Einstein Manifolds
• On perturbative instability of Pope-Warner solutions on Sasaki-Einstein manifolds
• Warped Resolved L^{a,b,c} Cones
• Superconformal Symmetry in the Kaluza-Klein Spectrum of Warped AdS(3)
• Massless geodesics in $Ad{S}_5\times Y(p,q)$ as a superintegrable system
• On Exactly Marginal Deformations Dual to $B$-Field Moduli of IIB Theory on SE${}_5$
• Triangle Anomalies from Einstein Manifolds
• On the Scalar Spectrum of the Y^{p,q} Manifolds
• Generalized Area Law under Multi-parameter Rotating Black Hole Spacetime
• Holographic spectral functions for Sasaki-Einstein 5-manifolds