Green's functions and non-singlet glueballs on deformed conifolds

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 Cd through the equation Σdi=1zi2 = ε2. We discuss Green's function with a source at a point on the Sd-1 zero section of TSd-1. Its calculation is complicated by mixing between different harmonics with the same SO(d) quantum numbers due to the explicit breaking by the ε-deformation of the U(1) symmetry that rotates zi 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.