Green's Functions and Non-Singlet Glueballs on Deformed Conifolds

TL;DR

This paper investigates the Green's functions and spectra of non-singlet glueballs on deformed conifolds, using numerical methods to analyze the effects of symmetry breaking in higher-dimensional Ricci-flat spaces relevant to gauge/gravity duality.

Contribution

It introduces a numerical approach to solve the mixing of harmonics caused by symmetry breaking in deformed conifolds, advancing understanding of bound states in gauge/gravity duality.

Findings

Calculated Green's functions with sources on S^{d-1} zero sections.

Determined bound state spectra in SO(d) representations for d=4 and d=5.

Analyzed effects of symmetry breaking on harmonic mixing and spectra.

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 \sum_{i = 1}^d {z_i^2} = \epsilon^2. We discuss the Green's function with a source at a point on the S^{d-1} zero section of TS^{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 \epsilon-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.