On the spectra of holographic QFTs on constant curvature manifolds

TL;DR

This paper studies the spectra of scalar and tensor fluctuations in holographic QFTs on curved spacetimes, revealing discrete spectra in negative curvature and continuous spectra in positive curvature, with numerical analysis confirming stability in a specific model.

Contribution

It provides a detailed analysis of fluctuation spectra in holographic QFTs on (A)dS spaces, including eigenvalue equations and numerical results for a concrete model.

Findings

Negative curvature yields discrete spectra.

Positive curvature leads to continuous spectra starting at a specific mass squared.

Numerical analysis shows no instabilities in the studied model.

Abstract

We analyze linear fluctuations of five-dimensional Einstein-Dilaton theories dual to holographic quantum field theories defined on four-dimensional de Sitter and Anti-de Sitter space-times. We identify the physical propagating scalar and tensor degrees of freedom. For these, we write the linearized bulk field equations as eigenvalue equations. In the dual QFT, the eigenstates correspond to towers of spin-0 and spin-2 particles propagating on $(A)dS_4$ associated to gauge-invariant composite states. Using particular care in treating special ``zero-modes,'' we show in general that, for negative curvature, the particle spectra are always discrete, whereas for positive curvature they always have a continuous component starting at $m^2 = (9/4)\alpha^{-2}$, where $\alpha$ is the $(A)dS_4$ radius. We numerically compute the spectra in a concrete model characterized by a polynomial dilaton bulk potential admitting holographic RG-flow solutions with a UV and IR fixed points. In this case, we find no discrete spectrum and no perturbative instabilities.