Relevant Dilaton Stabilization

TL;DR

This paper introduces a modified stabilization mechanism for conformal theories using a relevant operator, resulting in a stronger phase transition and weaker gravitational wave signals, with potential observability.

Contribution

It proposes a new stabilization approach using a relevant operator, altering the phase transition dynamics and gravitational wave predictions in conformal models.

Findings

Reduced bounce action leads to a weaker first-order phase transition.

Gravitational wave signals are diminished but may still be detectable.

The mechanism is natural if the explicit breaking source is the only symmetry-breaking term.

Abstract

We propose a simple modification of the Goldberger-Wise mechanism for stabilizing the scale of spontaneously broken conformal theories. The source of explicit conformal symmetry breaking is a relevant operator with a small coefficient, as opposed to the usual mechanism of an almost marginal operator with an order-one coefficient. In the warped 5D picture this relevant stabilization corresponds to a small tadpole for the bulk scalar on the UV brane, which can be technically natural if it is the only source for the breaking of a symmetry (for example, a discrete $Z_2$). This modification of the stabilization mechanism has significant consequences for the nature of the conformal phase transition, since the radion/dilaton potential is no longer shallow. The bounce action is significantly reduced, leading to a weaker first-order phase transition instead of the supercooled and strongly first-order transition seen in Goldberger-Wise stabilization. This also leads to reduction of gravitational wave signals which, however, may still be observable at future detectors. We present numerical and analytical studies of the phase transition and the resulting gravitational wave signal strength, assuming that the effective dilaton potential provides a good leading approximation. While the dilaton is not expected to be generically light in this setup, in order to keep perturbative control over the effective theory one needs to mildly tune the dilaton quartic to be somewhat small.