A naturally light dilaton and a small cosmological constant.

Brando Bellazzini,Jay Hubisz,Csaba Csáki,Javi Serra,John Terning

doi:10.1140/epjc/s10052-014-2790-x

Abstract

We present a non-supersymmetric theory with a naturally light dilaton. It is based on a 5D holographic description of a conformal theory perturbed by a close-to-marginal operator of dimension 4-epsilon which develops a condensate. As long as the dimension of the perturbing operator remains very close to marginal (even for large couplings) a stable minimum at hierarchically small scales is achieved, where the dilaton mass squared is suppressed by epsilon . At the same time the cosmological constant in this sector is also suppressed by epsilon , and thus it is parametrically smaller than in a broken SUSY theory. As a byproduct we also present an exact solution to the scalar-gravity system that can be interpreted as a new holographic realization of spontaneously broken conformal symmetry. Even though this metric deviates substantially from AdS space in the deep IR it still describes a non-linearly realized exactly conformal theory. We also display the effective potential for the dilaton for arbitrary holographic backgrounds.

Highlights

We present a non-supersymmetric theory with a naturally light dilaton
One possible scenario is that conformality is spontaneously broken along a flat direction, which is lifted via the potential generated through a small external coupling whose non-zero and small β-function breaks scale invariance explicitly
This mechanism is essentially what is assumed to happen in the Randall–Sundrum (RS) model [4] stabilized via the Goldberger–Wise (GW) mechanism [5]: the bulk scalar field is associated with the small and slowly running external coupling, and the appearance of the IR brane signals that spontaneous breaking of scale invariance (SBSI) has occurred [6,7]

Summary

Introduction

C (2014) 74:2790 come if the quartic becomes mildly energy dependent via an explicit scale-invariance breaking perturbation, whose β-function remains parametrically small, but not necessarily the coupling itself In this case the expectation is that SBSI will happen around the scale where the effective dilaton quartic vanishes, which can be a hierarchically small scale if the running lasts for a long time. This way we will be able to explicitly calculate the effective dilaton potential and show that the mass is suppressed by the small parameter of the β-function at the minimum of the potential This yields an explicit construction for a dilaton that is parametrically lighter than the dynamical scale of the theory as required for models where the dilaton is a Higgs-like particle [12,13,14,19,20,21]. Page 3 of 16 2790 to an alternative derivation of the dilaton effective potential (Appendix A), the detailed derivation of the small backreaction case (Appendix B) and the GW case (Appendix C), an explanation of the asymptotic matching procedure for the boundary layer problem used for finding the full solution (Appendix D), a discussion of the dilaton kinetic term as well as dilaton parametrizations (Appendix E), and a discussion of an alternative choice for the IR brane potential (Appendix F)

Light dilatons via long running and small β-function

The dilaton effective potential in holographic models

Constant bulk potential–flat dilaton potential by tuning two condensates

Light dilaton without tuning: the general case

Dilaton reparametrizations