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QCD and dimensional deconstruction

D. T. Son, M. A. Stephanov

TL;DR

The paper develops an open moose model with $K$ hidden gauge groups to realize dimensional deconstruction of a $4+1$ dimensional gauge theory relevant to QCD-like dynamics. In the $K\to\infty$ limit, the theory becomes a $4+1$ dimensional Yang–Mills theory in a curved background with two boundaries, enabling a controlled description of vector mesons, pion dynamics, and current correlators, with an AdS/CFT–like prescription emerging for boundary sources. The authors derive closed-form expressions for the pion decay constant $f_\pi$, vector/axial-vector masses $m_n$, decay constants $g_{nV}, g_{nA}$, and couplings $g_{n\pi\pi}$, verify Weinberg sum rules, and analyze the pion form factor $G_{V\pi\pi}(q)$ showing (exact) vector meson dominance in suitable backgrounds. They present exactly solvable backgrounds, including flat and cosh metrics, to illustrate the qualitative and quantitative phenomenology and to connect hadron parameters to the QCD scale via a holographic-like framework. Overall, the work provides a bridge between hidden local symmetry approaches, dimensional deconstruction, and holographic ideas, offering a potential 5D dual perspective on QCD.

Abstract

Motivated by phenomenological models of hidden local symmetries and the ideas of dimensional deconstruction and gauge/gravity duality, we consider the model of an "open moose". Such a model has a large number K of hidden gauge groups as well as a global chiral symmetry. In the continuum limit K->infinity the model becomes a 4+1 dimensional theory of a gauge field propagating in a dilaton background and an external space-time metric with two boundaries. We show that the model reproduces several well known phenomenological and theoretical aspects of low-energy hadron dynamics. We derive the general formulas for the mass spectrum, the decay constants of the pion and vector mesons, and the couplings between mesons. We then consider two simple realizations, one with a flat metric and another with a "cosh" metric interpolating between two AdS boundaries. For the pion form-factor, the single pole rho-meson dominance is exact in the latter case and approximate in the former case. We discover that an AdS/CFT-like prescription emerges in the computation of current-current correlators. We speculate on the role of the model in the theory dual to QCD.

QCD and dimensional deconstruction

TL;DR

The paper develops an open moose model with hidden gauge groups to realize dimensional deconstruction of a dimensional gauge theory relevant to QCD-like dynamics. In the limit, the theory becomes a dimensional Yang–Mills theory in a curved background with two boundaries, enabling a controlled description of vector mesons, pion dynamics, and current correlators, with an AdS/CFT–like prescription emerging for boundary sources. The authors derive closed-form expressions for the pion decay constant , vector/axial-vector masses , decay constants , and couplings , verify Weinberg sum rules, and analyze the pion form factor showing (exact) vector meson dominance in suitable backgrounds. They present exactly solvable backgrounds, including flat and cosh metrics, to illustrate the qualitative and quantitative phenomenology and to connect hadron parameters to the QCD scale via a holographic-like framework. Overall, the work provides a bridge between hidden local symmetry approaches, dimensional deconstruction, and holographic ideas, offering a potential 5D dual perspective on QCD.

Abstract

Motivated by phenomenological models of hidden local symmetries and the ideas of dimensional deconstruction and gauge/gravity duality, we consider the model of an "open moose". Such a model has a large number K of hidden gauge groups as well as a global chiral symmetry. In the continuum limit K->infinity the model becomes a 4+1 dimensional theory of a gauge field propagating in a dilaton background and an external space-time metric with two boundaries. We show that the model reproduces several well known phenomenological and theoretical aspects of low-energy hadron dynamics. We derive the general formulas for the mass spectrum, the decay constants of the pion and vector mesons, and the couplings between mesons. We then consider two simple realizations, one with a flat metric and another with a "cosh" metric interpolating between two AdS boundaries. For the pion form-factor, the single pole rho-meson dominance is exact in the latter case and approximate in the former case. We discover that an AdS/CFT-like prescription emerges in the computation of current-current correlators. We speculate on the role of the model in the theory dual to QCD.

Paper Structure

This paper contains 15 sections, 72 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The open moose
  3. Physical observables
  4. Pion decay constant $f_\pi$
  5. Vector meson mass spectrum $m_n$
  6. Vector meson-pion-pion coupling $g_{n\pi\pi}$
  7. Vector meson decay constants $g_{nV}$ and $g_{nA}$
  8. Spectral sum rules
  9. Pion form factor and VMD
  10. $K\to\infty$ and continuum limit
  11. Physical observables
  12. $d=4+1$ and dimensional deconstruction
  13. AdS/CFT connection
  14. Exactly solvable examples and phenomenology
  15. Example I: flat background

Figures (2)

  • Figure 1: Graphic representation of the Lagrangian (\ref{['L']}). The examples of low $K$ corresponding to previously considered theories are also shown. $K=0$ represents Weinberg's nonlinear sigma model for pions; $K=1$ represents a hidden symmetry Lagrangian describing $\pi$ and $\rho$; and $K=2$ represents a description of $\pi$, $\rho$, and $a_1$HLSHLSa1.
  • Figure :