Fang Chen, Keshav Dasgupta, Alberto Enciso, Niky Kamran, Jihye Seo
The spectra of supergravity modes in anti de Sitter (AdS) space on a
five-sphere endowed with the round metric (which is the simplest 5d
Sasaki-Einstein space) has been studied in detail in the past. However for the
more 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 been
attempted. Earlier studies on scalar spectrum were restricted to only the first
few eigenstates. In this paper we take a step in this direction by analysing
the full scalar spectrum on these spaces. However it turns out that finding the
exact solution of the corresponding eigenvalue problem in closed form is not
feasible since the computation of the eigenvalues of the Laplacian boils down
to the analysis of a one-dimensional operator of Heun type, whose spectrum
cannot be computed in closed form. However, despite this analytical obstacle,
we manage to get both lower and upper bounds on the eigenvalues of the scalar
spectrum by comparing the eigenvalue problem with a simpler, solvable system.
We also briefly touch upon various other new avenues such as non-commutative
and dipole deformations as well as possible non-conformal extensions of these
models.
View original:
http://arxiv.org/abs/1201.5394
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