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A Naturally Light Dilaton and a Small Cosmological Constant

B. Bellazzini, C. Csaki, J. Hubisz, J. Serra, J. Terning

TL;DR

The paper addresses how to obtain a naturally light dilaton and a small cosmological constant in a non-supersymmetric framework by embedding the problem in a 5D holographic model. It shows that perturbing a conformal theory with a near-marginal operator (dimension 4-\epsilon) and allowing slow RG running produces SBSI with a dilaton mass and vacuum energy suppressed by \epsilon. A key result is the general dilaton effective potential V_eff(\\chi) = \\chi^4 F(\\lambda(\\chi)) and its boundary-driven structure, which yields a light dilaton even without fine-tuned flat directions. The work also provides an exact solution for a dimension-4 condensate and discusses how two-condensate tuning can flatten the potential, highlighting the mechanism’s potential and its limitations for addressing the cosmological constant problem in realistic settings.

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 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.

A Naturally Light Dilaton and a Small Cosmological Constant

TL;DR

The paper addresses how to obtain a naturally light dilaton and a small cosmological constant in a non-supersymmetric framework by embedding the problem in a 5D holographic model. It shows that perturbing a conformal theory with a near-marginal operator (dimension 4-\epsilon) and allowing slow RG running produces SBSI with a dilaton mass and vacuum energy suppressed by \epsilon. A key result is the general dilaton effective potential V_eff(\\chi) = \\chi^4 F(\\lambda(\\chi)) and its boundary-driven structure, which yields a light dilaton even without fine-tuned flat directions. The work also provides an exact solution for a dimension-4 condensate and discusses how two-condensate tuning can flatten the potential, highlighting the mechanism’s potential and its limitations for addressing the cosmological constant problem in realistic settings.

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 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.

Paper Structure

This paper contains 13 sections, 100 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Light dilatons via long running and small $\beta$-function
  3. The dilaton effective potential in holographic models
  4. Constant bulk potential - flat dilaton potential by tuning two condensates
  5. Light dilaton without tuning: the general case
  6. Conclusions
  7. Effective potential and boundary terms
  8. The massless case for small back-reaction
  9. (Mistuned) Goldberger-Wise revisited
  10. Asymptotic matching
  11. Dilaton kinetic term
  12. Dilaton reparametrizations
  13. Linear IR potential

Figures (3)

  • Figure 1: Pictorial representation of the tuned scenario with vanishing quartic in the absence of stabilizing perturbation (left) versus the proposal discussed in this work, where a large perturbation compensates for the large initial quartic (right).
  • Figure 2: Left, bulk scalar profile: $\phi_{full}$ (solid black), $\phi_{r}$ (dashed red), and $\phi_b$ (dotted blue). Right, effective AdS curvature, $A'(y)$: same color code.
  • Figure 3: The plot of the effective dilaton potential Eq. (\ref{['eq:IRpot']}) for the parameters $\epsilon=0.1$, $v_0=0.1$, $v_1=4.5$, $\Lambda_1 = - 50$, $\mu_0 = 1$, and $\kappa = 0.5$, all of them in units $k=1$. The plot in the right is a zoom of the region where the minimum of the potential is.