Interpolating between low and high energy QCD via a 5D Yang-Mills model

TL;DR

This work constructs a holographic 5D SU$(N_f) imes$SU$(N_f)$ Yang–Mills model in a finite interval to describe massless pions and an infinite tower of spin-1 resonances, bridging χPT at low energy with perturbative QCD at high energy. Through a careful chiral implementation of the holographic recipe, the authors derive a generating functional that yields the correct Ward identities and separates sources from dynamical fields, enabling explicit predictions for the χPT LECs, resonance couplings, and two-point functions. The model automatically imposes sum rules that ensure soft high-energy behavior, yields unsubtracted dispersion relations for the vector form factor, and reproduces the partonic log in the UV while allowing controlled deformations to generate condensates. Overall, the framework provides a tractable, analytic interpolation across energy scales with clear 5D origins for the resonance structure and high-energy constraints, offering insights into vector/axial sectors and Weinberg sum rules while highlighting metric-dependence aspects.

Abstract

We describe the Goldstone bosons of massless QCD together with an infinite number of spin-1 mesons. The field content of the model is SU(Nf)xSU(Nf) Yang-Mills in a compact extra-dimension. Electroweak interactions reside on one brane. Breaking of chiral symmetry occurs due to the boundary conditions on the other brane, away from our world, and is therefore spontaneous. Our implementation of the holographic recipe maintains chiral symmetry explicit throughout. For intermediate energies, we extract resonance couplings. These satisfy sum rules due to the 5D nature of the model. These sum rules imply, when taking the high energy limit, that perturbative QCD constraints are satisfied. We also illustrate how the 5D model implies a definite prescription for handling infinite sums over 4D resonances. Taking the low energy limit, we recover the chiral expansion and the corresponding non-local order parameters. All local order parameters are introduced separately.