A naturally light dilaton and a small cosmological constant

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 [Formula: see text] 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 [Formula: see text] . At the same time the cosmological constant in this sector is also suppressed by [Formula: see text] , 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.