A rapid holographic phase transition with brane-localized curvature

TL;DR

This work analyzes finite-temperature dynamics of the RS I model with TeV-brane localized curvature, showing that the brane curvature rescales the radion kinetic term and, when combined with Goldberger-Wise stabilization, enables a holographic first-order phase transition at much larger $N$ than previously possible. The study maps the thermal transition to a Hawking-Page–like competition between planar AdS black hole and the stabilized RS geometry, with the radion acting as the order parameter and its kinetics controlling tunneling. By exploring parameter space and introducing xi_IR, the authors demonstrate that nucleation can occur with moderate supercooling even at large N, and they examine the phenomenological consequences for radion and KK graviton spectra, including suppressed KK masses and TeV-scale radion couplings that face current collider constraints. The results provide a self-consistent cosmological history and predict distinctive low-energy signatures, while highlighting uncertainties in the high-temperature (BH) sector that merit further gravitational instanton analysis.

Abstract

We study the finite-temperature properties of the Randall-Sundrum model in the presence of brane-localized curvature. At high temperature, as dictated by AdS/CFT, the theory is in a confined phase dual to the planar AdS black hole. When the radion is stabilized, à la Goldberger-Wise, a holographic first-order phase transition proceeds. The brane-localized curvature contributes to the radion kinetic energy, substantially decreasing the critical bubble energy. Contrary to previous results, the phase transition completes at much larger values of $N$, the number of degrees of freedom in the CFT. Moreover, the field value of the bulk scalar on the TeV-brane is allowed to become large, while remaining consistent with back-reaction constraints. Assisted by this fact, we find that for a wide region in the parameter space tunneling happens rather quickly, i.e. the nucleation temperature becomes of the order of the critical temperature. At zero temperature, the most important signature of brane-localized curvature is the reduction of spin-2 Kaluza-Klein graviton masses and a heavier radion.

Figures (14)

• Figure 1: A plot of the radion potential, described by Eq. \ref{['finLag']}, for $\Phi_T=1,\ \epsilon=0.1$ and $(M_\star l) = 0.55$. The inset shows the size and location of the maximum.
• Figure 2: The dependence of various quantities in the bounce action $S_3/T$ of Eq. \ref{['s3overTdecomp']} on $(M_\star l)$ for a range of release points. We take the benchmark values $\epsilon = 0.05$ and $\Phi_T = 1$.
• Figure 3: The bounce action $S_3/T$ for various values of $(M_\star l)$ with the benchmark values $\epsilon = 0.05$ and $\Phi_T = 1$, where the blue line represents the nucleation condition. It is clear that increasing $(M_\star l)$ hinders the tunneling.
• Figure 4: The dependence of various quantities in the bounce action $S_3/T$ of Eq. \ref{['s3overTdecomp']} on $\Phi_T$ for a range of release points. We take the benchmark values $\epsilon = 0.05$ and $(M_\star l) = 0.55$.
• Figure 5: The bounce action $S_3/T$ for various values of $\Phi_T$ with the benchmark values $\epsilon = 0.05$ and $(M_\star l)=0.55$, where the blue line represents the nucleation condition. It is clear that increasing $\Phi_T$ significantly improves nucleation rates.