Abstract
We present an holographic approach to strongly-coupled theories close to the conformal to non-conformal transition, trying to understand the presence of light scalars as recent lattice simulations seem to suggest. We find that the dilaton is always the lightest resonance, although not parametrically lighter than the others. We provide a simple analytic formula for the dilaton mass that allows us to understand this behavior. The pattern of the meson mass spectrum, as we get close to the conformal transition, is found to be quite similar to that in lattice simulations. We provide further predictions from holography that can be checked in the future. These five-dimensional models can also implement new solutions to the hierarchy problem, having implications for searches at the LHC and cosmology.
Highlights
Recent lattice simulations suggest that, contrary to real QCD, theories close to the conformal transition have as the lightest resonance a 0++ state [1,2,3,4,5]
We present an holographic approach to strongly-coupled theories close to the conformal to non-conformal transition, trying to understand the presence of light scalars as recent lattice simulations seem to suggest
Close to the conformal edge the theory contains a marginal operator Og whose dimension gets a small imaginary part when conformal invariance is lost. Assuming that this is the case, the AdS/conformal field theory (CFT) correspondence [7,8,9] can provide a simple realization of this idea as a complex operator dimension matches to a scalar having a mass below the Breitenlohner-Freedman (BF) bound MΦ2 = −4/L2
Summary
There are several ways to lose an IR fixed point as we move the parameters of the theory. [6] we will consider conformal transitions characterized by the third case, the merging of the IR fixed point with a UV fixed point, as depicted in figure 1. The qqoperator whose dimension will go from ∼ 3 when entering the conformal window (at the Banks-Zaks fixed point) to 2 when leaving it at the other side when it becomes complex. When the theory is close but outside the conformal window (i.e. 0 < 1), one can calculate the RG flow “time” required to cross the region where g ∼ g∗ and |βg| 1. This gives us the IR-scale ΛIR at which the theory is expected to confine as g becomes large. Eq (2.5) is usually referred as walking or Miransky scaling
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