Holographic gauged NJL model: the conformal window and ideal walking

Abstract

We study the holographic dynamic anti-de Sitter/QCD description of a SU(Nc) non-Abelian gauge theory with Nf fermions in the fundamental representation which also have Nambu–Jona-Lasinio (NJL) interactions included using Witten’s multitrace prescription. In particular, here, we study aspects of the dynamics in and near the conformal window of the gauge theory as described by the two-loop running of the gauge theory. If the number of flavors is such that the IR fixed point lies with the anomalous dimension, γ, of the quark bilinear above one, then chiral symmetry breaking occurs. Here, we display a spiral in the quark mass/condensate plane describing a sequence of unstable excited states of the vacuum. An attractive NJL operator enhances the vacuum condensate, but only an infinitely repulsive NJL interaction switches off the condensation completely. When Nf changes so that the IR fixed point falls below 1 (the conformal window region), there is a numerical discontinuity in the phase structure with condensation only occurring with a supercritical NJL interaction. In the conformal window, the running of γ to a nontrivial IR fixed point is similar to walking dynamics, although chiral symmetry breaking is not triggered. In the “ideal walking” scenario, chiral symmetry is broken in that IR conformal regime by the NJL interaction, but the change in γ enhances the UV condensate. That enhancement of the condensate is shown in an analytic model with a sharp change in γ, and we show equivalent numerical results for the case of the two-loop running. In the model, the σ becomes massless as the gauge theory running becomes near conformal, and we show it is possible to realize a light Higgs-like state in ideal walking models.

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