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

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

2005-05-30

arxiv.org/abs/hep-th/0505259v2

Phys.Lett. B621 (2005) 288-294

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, references added

Scientific paper

10.1016/j.physletb.2005.06.061

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.

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