Holography of the Conformal Window

TL;DR

This paper develops holographic models to study the onset of chiral symmetry breaking near the conformal window in QCD, revealing phase transitions influenced by running coupling and anomalous dimensions.

Contribution

It introduces two holographic models incorporating QCD running coupling and anomalous dimensions to analyze chiral symmetry breaking at the conformal window edge.

Findings

Chiral symmetry breaks for N_f/N_c<2.9 in the naive model.

Imposing QCD anomalous dimensions yields a BKT transition at N_f/N_c=4.

Transition occurs when the anomalous dimension _m=1.

Abstract

Inspired by the model of Jarvinen and Kiritsis, we present a simple holographic model for the on set of chiral symmetry breaking at the edge of the conformal window in QCD in the Veneziano limit. Our most naive model enforces the QCD two loop running coupling on a D3/D7 holographic brane system. The mass of the holographic field, describing the chiral condensate in the model, is driven below the BF bound when the running is sufficiently strong, triggering chiral symmetry breaking for N_f/N_c<2.9. This model though contains too great a remnant of supersymmetry and does not correctly encode the perturbative anomalous dimensions of QCD. In a second model we impose the QCD anomalous dimension result and find chiral symmetry breaking sets in for N_f/N_c=4 at a BKT-type phase transition. In this case the transition is triggered when the anomalous dimension of the mass operator \gamma_m=1.