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Holography and the Electroweak Phase Transition

Paolo Creminelli, Alberto Nicolis, Riccardo Rattazzi

TL;DR

This work uses holography to study the finite-temperature phases of the compact Randall-Sundrum model with radius stabilization. The high-temperature phase is AdS$_5$-Schwarzschild (a hot CFT) while the low-temperature phase is the RS solution with the TeV brane, with a first-order transition at $T_c$ set by the Goldberger-Wise potential. For weak stabilization, $T_c$ is parametrically below the TeV scale, causing a slow transition that can trigger a brief inflation-like epoch at the weak scale; the cosmological evolution critically depends on the stabilization details and can be viable only for sufficiently strong stabilization or altered model parameters. The analysis connects 5D gravitational solutions to 4D CFT dynamics, providing quantitative constraints on phase-transition rates via radion-dominated tunneling and offering insights into early-Universe cosmology in warped extra dimensions.

Abstract

We study through holography the compact Randall-Sundrum (RS) model at finite temperature. In the presence of radius stabilization, the system is described at low enough temperature by the RS solution. At high temperature it is described by the AdS-Schwarzschild solution with an event horizon replacing the TeV brane. We calculate the transition temperature T_c between the two phases and we find it to be somewhat smaller than the TeV scale. Assuming that the Universe starts out at T >> T_c and cools down by expansion, we study the rate of the transition to the RS phase. We find that the transition is very slow so that an inflationary phase at the weak scale begins. The subsequent evolution depends on the stabilization mechanism: in the simplest Goldberger-Wise case inflation goes on forever unless tight bounds are satisfied by the model parameters; in slightly less-minimal cases these bounds may be relaxed.

Holography and the Electroweak Phase Transition

TL;DR

This work uses holography to study the finite-temperature phases of the compact Randall-Sundrum model with radius stabilization. The high-temperature phase is AdS-Schwarzschild (a hot CFT) while the low-temperature phase is the RS solution with the TeV brane, with a first-order transition at set by the Goldberger-Wise potential. For weak stabilization, is parametrically below the TeV scale, causing a slow transition that can trigger a brief inflation-like epoch at the weak scale; the cosmological evolution critically depends on the stabilization details and can be viable only for sufficiently strong stabilization or altered model parameters. The analysis connects 5D gravitational solutions to 4D CFT dynamics, providing quantitative constraints on phase-transition rates via radion-dominated tunneling and offering insights into early-Universe cosmology in warped extra dimensions.

Abstract

We study through holography the compact Randall-Sundrum (RS) model at finite temperature. In the presence of radius stabilization, the system is described at low enough temperature by the RS solution. At high temperature it is described by the AdS-Schwarzschild solution with an event horizon replacing the TeV brane. We calculate the transition temperature T_c between the two phases and we find it to be somewhat smaller than the TeV scale. Assuming that the Universe starts out at T >> T_c and cools down by expansion, we study the rate of the transition to the RS phase. We find that the transition is very slow so that an inflationary phase at the weak scale begins. The subsequent evolution depends on the stabilization mechanism: in the simplest Goldberger-Wise case inflation goes on forever unless tight bounds are satisfied by the model parameters; in slightly less-minimal cases these bounds may be relaxed.

Paper Structure

This paper contains 11 sections, 64 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The RS model at finite temperature
  3. Two gravity solutions
  4. The free energy of the black hole solution
  5. The effect of the Goldberger-Wise field
  6. Computation of the transition temperature
  7. Dynamics of the phase transition
  8. Thin wall approximation
  9. Conclusions and outlook
  10. Acknowledgments
  11. A radion driven cosmology

Figures (3)

  • Figure 1: 5D picture of the 4D bubble configuration. The two solutions are connected by moving the black hole horizon and the TeV brane towards the AdS infinity.
  • Figure 2: The topology of the bubble. We have suppressed two spatial dimensions, so that the AdS-S solution is a cylinder: the bubble appears as hole in the cylinder. The rotational invariance is here seen as a discrete ${\mathbb Z}_2$ inversion symmetry.
  • Figure 3: The free energy for the RS solution (right side) and the black hole one (left). RS model is parametrized by the radion VEV $\mu$, while the AdS-S one by the Hawking temperature $T_h$. The two classes of solutions coincide at $\mu = T_h = 0$.