Stability of the cascading gauge theory de Sitter DFPs

Abstract

We study stability of the Dynamical Fixed Points (DFPs) of the cascading gauge theory at strong coupling in de Sitter space-time. We compute the spectra of the perturbative fluctuations and identify stable/unstable DFPs, characterized by the ratio of the strong coupling scale $\Lambda$ of the gauge theory and the Hubble constant $H$ of the background space-time. We discover a new phenomenon in the spectrum of gravitational fluctuations of a non-conformal holographic model: distinct branches of the fluctuations for $H\gg \Lambda$ coalesce for sufficiently low $\frac{H}{\Lambda}$, leading to the removal of some excited modes from the spectrum. We establish that, at least in a dual supergravity approximation, cascading gauge theory does not have a stable DFP for $H\in (H_{crit_1},H_{crit_2})$. Initial states of the theory for $H>H_{crit_2}$ evolve to a stable DFP with unbroken chiral symmetry; while for $H< H_{crit_1}$ the states evolve to a de Sitter vacuum with spontaneously broken chiral symmetry.