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More on a holographic dual of QCD

Tadakatsu Sakai, Shigeki Sugimoto

TL;DR

This work analyzes a holographic dual of massless QCD based on D4/D8-branes to derive the 4D effective action for pions and an infinite tower of vector mesons coupled to external gauge fields. It demonstrates strong vector meson dominance in the pion form factor and the WZW sector, and derives KSRF-type relations, Skyrme coefficients, and Weinberg-like sum rules within the five-dimensional YM+CS framework. Numerical estimates show reasonable, though not perfect, agreement with experimental values, highlighting rho-dominance in key observables while also exposing areas requiring corrections beyond the leading large-N_c, large-λ limit. The results support the qualitative and semi-quantitative utility of holographic QCD models for low-energy hadronic phenomenology and outline avenues for refinement via higher-order corrections and backreaction effects.

Abstract

We investigate the interactions among the pion, vector mesons and external gauge fields in the holographic dual of massless QCD proposed in a previous paper, hep-th/0412141, on the basis of probe D8-branes embedded in a D4-brane background in type IIA string theory. We obtain the coupling constants by performing both analytic and numerical calculations, and compare them with experimental data. It is found that the vector meson dominance in the pion form factor as well as in the Wess-Zumino-Witten term holds in an intriguing manner. We also study the ωto πγand ωto 3πdecay amplitudes. It is shown that the interactions relevant to these decay amplitudes have the same structure as that proposed by Fujiwara et al. Various relations among the masses and the coupling constants of an infinite tower of mesons are derived. These relations play crucial roles in the analysis. We find that most of the results are consistent with experiments.

More on a holographic dual of QCD

TL;DR

This work analyzes a holographic dual of massless QCD based on D4/D8-branes to derive the 4D effective action for pions and an infinite tower of vector mesons coupled to external gauge fields. It demonstrates strong vector meson dominance in the pion form factor and the WZW sector, and derives KSRF-type relations, Skyrme coefficients, and Weinberg-like sum rules within the five-dimensional YM+CS framework. Numerical estimates show reasonable, though not perfect, agreement with experimental values, highlighting rho-dominance in key observables while also exposing areas requiring corrections beyond the leading large-N_c, large-λ limit. The results support the qualitative and semi-quantitative utility of holographic QCD models for low-energy hadronic phenomenology and outline avenues for refinement via higher-order corrections and backreaction effects.

Abstract

We investigate the interactions among the pion, vector mesons and external gauge fields in the holographic dual of massless QCD proposed in a previous paper, hep-th/0412141, on the basis of probe D8-branes embedded in a D4-brane background in type IIA string theory. We obtain the coupling constants by performing both analytic and numerical calculations, and compare them with experimental data. It is found that the vector meson dominance in the pion form factor as well as in the Wess-Zumino-Witten term holds in an intriguing manner. We also study the ωto πγand ωto 3πdecay amplitudes. It is shown that the interactions relevant to these decay amplitudes have the same structure as that proposed by Fujiwara et al. Various relations among the masses and the coupling constants of an infinite tower of mesons are derived. These relations play crucial roles in the analysis. We find that most of the results are consistent with experiments.

Paper Structure

This paper contains 19 sections, 174 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The model
  3. DBI part
  4. The effective action
  5. Numerical results
  6. The Skyrme term
  7. KSRF relations
  8. Electromagnetic form factors
  9. $a_1\rightarrow \pi\gamma$ and $a_1\rightarrow \pi\rho$ decay
  10. $\pi\pi$ scattering
  11. Weinberg sum rules
  12. WZW term
  13. $\pi vv$, $\pi v{\cal V}$ and $\pi{\cal V}{\cal V}$ vertices
  14. $v\pi^3$ and ${\cal V}\pi^3$ vertices
  15. $\omega\rightarrow\pi^0\gamma$ and $\omega\rightarrow\pi^0\pi^+\pi^-$ decay
  16. ...and 4 more sections

Figures (4)

  • Figure 1: Pion form factor.
  • Figure 2: The relevant diagrams for the $a_1\rightarrow \pi\gamma$ decay amplitude.
  • Figure 3: The relevant diagrams for the $\pi\pi$ scattering.
  • Figure 4: The relevant diagrams for (1) $\omega\rightarrow\pi\gamma$ and (2) $\omega\rightarrow\pi\pi\pi$.