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The spectra of supergravity modes in anti de Sitter (AdS) space on afive-sphere endowed with the round metric (which is the simplest 5dSasaki-Einstein space) has been studied in detail in the past. However for themore general class of cohomogeneity one Sasaki-Einstein metrics on S^2 x S^3,given by the Y^{p, q} class, a complete study of the spectra has not beenattempted. Earlier studies on scalar spectrum were restricted to only the firstfew eigenstates. In this paper we take a step in this direction by analysingthe full scalar spectrum on these spaces. However it turns out that finding theexact solution of the corresponding eigenvalue problem in closed form is notfeasible since the computation of the eigenvalues of the Laplacian boils downto the analysis of a one-dimensional operator of Heun type, whose spectrumcannot be computed in closed form. However, despite this analytical obstacle,we manage to get both lower and upper bounds on the eigenvalues of the scalarspectrum by comparing the eigenvalue problem with a simpler, solvable system.We also briefly touch upon various other new avenues such as non-commutativeand dipole deformations as well as possible non-conformal extensions of thesemodels.

On the Scalar Spectrum of the Y^{p,q} Manifolds