### Abstract

We study the Laplacian on Stenzel spaces (generalized deformed conifolds), which are tangent bundles of spheres endowed with Ricci flat metrics. The (2d - 2)-dimensional Stenzel space has SO(d) symmetry and can be embedded in ℂ^{d} through the equation Σ^{d}_{i=1} z ^{2}_{i} = ∈^{2}. We discuss Green's function with a source at a point on the S^{d-1} zero section of T S^{d-1}. Its calculation is complicated by mixing between different harmonics with the same SO(d) quantum numbers due to the explicit breaking by the ∈-deformation of the U (1) symmetry that rotates z_{i} by a phase. A similar mixing affects the spectrum of normal modes of warped deformed conifolds that appear in gauge/gravity duality. We solve the mixing problem numerically to determine certain bound state spectra in various representations of SO(d) for the d = 4 and d = 5 examples.

Original language | English (US) |
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Article number | 055404 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 44 |

Issue number | 5 |

DOIs | |

State | Published - Feb 4 2011 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*44*(5), [055404]. https://doi.org/10.1088/1751-8113/44/5/055404