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

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

2012-01-25

arxiv.org/abs/1201.5394v3

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, 1 eps figure, LaTeX; v2: typos corrected and references added; v3: Text rearranged and elaborated at some places, ty

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On the Scalar Spectrum of the Y^{p,q} Manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Scalar Spectrum of the Y^{p,q} Manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Scalar Spectrum of the Y^{p,q} Manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-444547