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 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.