Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Low energy hadron physics in holographic QCD

Tadakatsu Sakai, Shigeki Sugimoto

TL;DR

Using a D4/D8 holographic setup, the authors model massless QCD with N_f flavors in the probe limit. They show chiral symmetry breaking arises geometrically from D8-anti-D8 merging, yielding massless pions whose low-energy action matches the Skyrme model, and they extend the framework to include vector mesons with couplings consistent with hidden local symmetry and a KSRF-type relation. The Chern-Simons term reproduces the chiral anomaly and generates a WZW term, while the η' mass is derived via the Witten-Veneziano mechanism. Baryons emerge as Skyrmions identified with wrapped D4-branes, and the model provides a controlled large-N_c realization of low-energy hadron physics, though it has KK-scale artifacts and limitations of the supergravity/probe approximations.

Abstract

We present a holographic dual of four-dimensional, large N_c QCD with massless flavors. This model is constructed by placing N_f probe D8-branes into a D4 background, where supersymmetry is completely broken. The chiral symmetry breaking in QCD is manifested as a smooth interpolation of D8 - anti-D8 pairs in the supergravity background. The meson spectrum is examined by analyzing a five-dimensional Yang-Mills theory that originates from the non-Abelian DBI action of the probe D8-brane. It is found that our model yields massless pions, which are identified with Nambu-Goldstone bosons associated with the chiral symmetry breaking. We obtain the low-energy effective action of the pion field and show that it contains the usual kinetic term of the chiral Lagrangian and the Skyrme term. A brane configuration that defines a dynamical baryon is identified with the Skyrmion. We also derive the effective action including the lightest vector meson. Our model is closely related to that in the hidden local symmetry approach, and we obtain a Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin-type relation among the couplings. Furthermore, we investigate the Chern-Simons term on the probe brane and show that it leads to the Wess-Zumino-Witten term. The mass of the η' meson is also considered, and we formulate a simple derivation of the η' mass term satisfying the Witten-Veneziano formula from supergravity.

Low energy hadron physics in holographic QCD

TL;DR

Using a D4/D8 holographic setup, the authors model massless QCD with N_f flavors in the probe limit. They show chiral symmetry breaking arises geometrically from D8-anti-D8 merging, yielding massless pions whose low-energy action matches the Skyrme model, and they extend the framework to include vector mesons with couplings consistent with hidden local symmetry and a KSRF-type relation. The Chern-Simons term reproduces the chiral anomaly and generates a WZW term, while the η' mass is derived via the Witten-Veneziano mechanism. Baryons emerge as Skyrmions identified with wrapped D4-branes, and the model provides a controlled large-N_c realization of low-energy hadron physics, though it has KK-scale artifacts and limitations of the supergravity/probe approximations.

Abstract

We present a holographic dual of four-dimensional, large N_c QCD with massless flavors. This model is constructed by placing N_f probe D8-branes into a D4 background, where supersymmetry is completely broken. The chiral symmetry breaking in QCD is manifested as a smooth interpolation of D8 - anti-D8 pairs in the supergravity background. The meson spectrum is examined by analyzing a five-dimensional Yang-Mills theory that originates from the non-Abelian DBI action of the probe D8-brane. It is found that our model yields massless pions, which are identified with Nambu-Goldstone bosons associated with the chiral symmetry breaking. We obtain the low-energy effective action of the pion field and show that it contains the usual kinetic term of the chiral Lagrangian and the Skyrme term. A brane configuration that defines a dynamical baryon is identified with the Skyrmion. We also derive the effective action including the lightest vector meson. Our model is closely related to that in the hidden local symmetry approach, and we obtain a Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin-type relation among the couplings. Furthermore, we investigate the Chern-Simons term on the probe brane and show that it leads to the Wess-Zumino-Witten term. The mass of the η' meson is also considered, and we formulate a simple derivation of the η' mass term satisfying the Witten-Veneziano formula from supergravity.

Paper Structure

This paper contains 22 sections, 212 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. D4/D8/$\overline{\hbox{D ,}}\!\!\!$8 system
  3. Probe D8-brane
  4. The D4 background
  5. Probe D8-brane configuration
  6. Gauge field
  7. $A_z=0$ gauge
  8. Analysis of meson spectra
  9. Vector mesons
  10. Massive scalar mesons
  11. Multi-flavor case
  12. Fluctuation modes around multiple probe branes
  13. Pion effective action
  14. Including vector mesons
  15. Comparison to the hidden local symmetry approach
  16. ...and 7 more sections

Figures (1)

  • Figure 1: A sketch of D8 and $\overline{\hbox{D ,}}\!\!\!$8 branes.