QCD and a Holographic Model of Hadrons

QCD and a Holographic Model of Hadrons

20 Dec 2005 | Joshua Erlich, Emanuel Katz, Dam T. Son, Mikhail A. Stephanov
This paper presents a five-dimensional holographic model for QCD that successfully reproduces low-energy hadronic observables. The model is based on the AdS/CFT correspondence and incorporates chiral symmetry breaking, leading to the Gell-Mann–Oakes–Renner relation for the pion mass. The model uses a holographic dual of QCD, with fields corresponding to operators in the boundary theory. The 5D fields are chosen to reproduce the dynamics of chiral symmetry breaking, and the model has four free parameters, three of which are determined by experimental data: the rho meson mass, the pion mass, and the pion decay constant. The model predicts other low-energy hadronic observables with good accuracy, suggesting that QCD can be reformulated as a string theory in a higher-dimensional curved space. The model is based on a 5D metric, with the fifth coordinate corresponding to the energy scale. The IR cutoff is introduced at z = z_m, where spacetime ends, and the model is confining. The 5D action includes fields corresponding to the chiral symmetry breaking operators, and the gauge coupling is determined by matching to QCD. The model successfully reproduces the vector current two-point function and the axial current correlator, leading to the GOR relation. The model predicts the masses and decay constants of mesons, including the rho and a1 mesons. The pion decay constant is calculated using the holographic version of the QCD sum rules. The model is tested against experimental data, with a rms error of 15% for Model A and 9% for Model B, which includes all seven observables. The model is considered crude but shows good agreement with experimental data, suggesting that a more complete holographic description of QCD is possible. The model can be extended to include glue-ball spectra, power corrections, SU(3) chiral symmetry, the chiral anomaly, and running of the gauge coupling. The results suggest that the holographic model provides a useful framework for understanding QCD in a higher-dimensional curved space.This paper presents a five-dimensional holographic model for QCD that successfully reproduces low-energy hadronic observables. The model is based on the AdS/CFT correspondence and incorporates chiral symmetry breaking, leading to the Gell-Mann–Oakes–Renner relation for the pion mass. The model uses a holographic dual of QCD, with fields corresponding to operators in the boundary theory. The 5D fields are chosen to reproduce the dynamics of chiral symmetry breaking, and the model has four free parameters, three of which are determined by experimental data: the rho meson mass, the pion mass, and the pion decay constant. The model predicts other low-energy hadronic observables with good accuracy, suggesting that QCD can be reformulated as a string theory in a higher-dimensional curved space. The model is based on a 5D metric, with the fifth coordinate corresponding to the energy scale. The IR cutoff is introduced at z = z_m, where spacetime ends, and the model is confining. The 5D action includes fields corresponding to the chiral symmetry breaking operators, and the gauge coupling is determined by matching to QCD. The model successfully reproduces the vector current two-point function and the axial current correlator, leading to the GOR relation. The model predicts the masses and decay constants of mesons, including the rho and a1 mesons. The pion decay constant is calculated using the holographic version of the QCD sum rules. The model is tested against experimental data, with a rms error of 15% for Model A and 9% for Model B, which includes all seven observables. The model is considered crude but shows good agreement with experimental data, suggesting that a more complete holographic description of QCD is possible. The model can be extended to include glue-ball spectra, power corrections, SU(3) chiral symmetry, the chiral anomaly, and running of the gauge coupling. The results suggest that the holographic model provides a useful framework for understanding QCD in a higher-dimensional curved space.
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