Abstract
We discuss the presence of a light dilaton in CFTs deformed by a nearly-marginal operator O, in the holographic realizations consisting of confining RG flows that end on a soft wall. Generically, the deformations induce a condensate <O>, and the dilaton mode can be identified as the fluctuation of <O>. We obtain a mass formula for the dilaton as a certain average along the RG flow. The dilaton is naturally light whenever i) confinement is reached fast enough (such as via the condensation of O) and ii) the beta function is small (walking) at the condensation scale. These conditions are satisfied for a class of models with a bulk pseudo-Goldstone boson whose potential is nearly flat at small field and exponential at large field values. Thus, the recent observation by Contino, Pomarol and Rattazzi holds in CFTs with a single nearly-marginal operator. We also discuss the holographic method to compute the condensate <O>, based on solving the first-order nonlinear differential equation that the beta function satisfies.
Highlights
We discuss the holographic method to compute the condensate O, based on solving the first-order nonlinear differential equation that the beta function satisfies
We discuss the presence of a light dilaton in CFTs deformed by a nearlymarginal operator O, in the holographic realizations consisting of confining RG flows that end on a soft wall
The logical question, raised in [1,2,3], is: can there be a naturally light dilaton in QFTs that are close to conformally invariant (CI)? The simplest and closest to a CFT is a CFT deformed by a nearly-marginal operator (‘nearly-marginal deformation’ for short)
Summary
The other convenient choice is the ‘RG-gauge’ where the warp factor a is the coordinate. Since the warp factor a is what plays the role holographically of the renormalization scale μ, in this gauge the comparison with the field theory language is most convenient. Once the RG scale μ is identified with the warp factor, and since the value of φ close to the boundary is identified as the coupling strength of the deformation (the λ in eq (1.1)), one immediately identifies the holographic version of the beta function [10, 11, 35] as. From eq (2.10) it is clear that the domain walls (with V (φ) < 0 everywhere) map to flows with a bounded beta function, β2 < d(d − 1). Clear at this point is that a constant beta function maps into exponential superpotential and potential. The answer is still yes for certain types of flows
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