28 Aug 2007 | Tadakatsu SAKAI and Shigeki SUGIMOTO
The paper presents a holographic dual model of four-dimensional, large \(N_c\) QCD with massless flavors. The 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-$\overline{\mathrm{D}}8$ pairs in the supergravity background. The meson spectrum is analyzed by examining a five-dimensional Yang-Mills theory derived from the non-Abelian DBI action of the probe D8-brane. The model yields massless pions, identified as Nambu-Goldstone bosons associated with the chiral symmetry breaking. The low-energy effective action of the pion field is derived and shown to include the usual kinetic term of the chiral Lagrangian and the Skyrme term. A brane configuration that defines a dynamical baryon, the Skyrnion, is identified. The effective action is also generalized to include the lightest vector meson, and the model is shown to be closely related to the hidden local symmetry approach, leading to a Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin-type relation among the couplings. The Chern-Simons term on the probe brane is shown to yield the Wess-Zumino-Witten term, and the mass of the \(\eta'\) meson is derived from the supergravity perspective. The paper discusses the differences between the model and QCD, including the existence of the \(SO(5)\) symmetry and the appearance of exotic Kaluza-Klein modes.The paper presents a holographic dual model of four-dimensional, large \(N_c\) QCD with massless flavors. The 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-$\overline{\mathrm{D}}8$ pairs in the supergravity background. The meson spectrum is analyzed by examining a five-dimensional Yang-Mills theory derived from the non-Abelian DBI action of the probe D8-brane. The model yields massless pions, identified as Nambu-Goldstone bosons associated with the chiral symmetry breaking. The low-energy effective action of the pion field is derived and shown to include the usual kinetic term of the chiral Lagrangian and the Skyrme term. A brane configuration that defines a dynamical baryon, the Skyrnion, is identified. The effective action is also generalized to include the lightest vector meson, and the model is shown to be closely related to the hidden local symmetry approach, leading to a Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin-type relation among the couplings. The Chern-Simons term on the probe brane is shown to yield the Wess-Zumino-Witten term, and the mass of the \(\eta'\) meson is derived from the supergravity perspective. The paper discusses the differences between the model and QCD, including the existence of the \(SO(5)\) symmetry and the appearance of exotic Kaluza-Klein modes.