Scalar Laplacian on Sasaki–Einstein manifolds [formula omitted

Hironobu Kihara,Makoto Sakaguchi,Yukinori Yasui

doi:10.1016/j.physletb.2005.06.061

Hironobu Kihara, Makoto Sakaguchi + Show 1 more

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https://doi.org/10.1016/j.physletb.2005.06.061

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Abstract

We study the spectrum of the scalar Laplacian on the five-dimensional toric Sasaki–Einstein manifolds Yp,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.

Highlights

The AdS/CFT correspondence [1] has attracted much interest as a realization of the string theory/gauge theory correspondence. It predicts that string theory in AdS5 × X5 with X5 be Sasaki-Einstein is dual to N = 1 4-dimensional superconformal field theory
The authors of [4][5] clarified the N = 1 4-dimensional dual superconformal field theories of IR fixed points of toric quiver gauge theories. (Further developments in this subject include [6][7].) On the other hand, in the gravity side, semiclassical strings moving on the AdS5 × Y p,q geometry are shown to be useful to establish the AdS/CFT correspondence in [8]
We study the spectrum of the scalar Laplacian on the 5-dimensional Sasaki-Einstein manifolds Y p,q