Low Energy Hadron Physics in Holographic QCD

Low Energy Hadron Physics in Holographic QCD

28 Aug 2007 | Tadakatsu SAKAI and Shigeki SUGIMOTO
This paper presents a holographic dual 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{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 $ \eta' $ meson is also considered, and we formulate a simple derivation of the $ \eta' $ mass term satisfying the Witten-Veneziano formula from supergravity. The paper explores various aspects of massless QCD using the D4/D8 model. Among those of interest is the appearance of massless pions as the Nambu-Goldstone bosons associated with the spontaneous chiral $ U(N_f)_{L} \times U(N_f)_{R} $ symmetry breaking. In fact, we find massless pseudo-scalar mesons in the meson spectrum. We derive the low-energy effective action of the massless pions and show that it is identical to that of the Skyrme model, which consists of the chiral Lagrangian including the Skyrme term. The Skyrme term was introduced by Skyrme to stabilize the soliton solution in the non-linear sigma model. It was proposed that this soliton, called a Skyrmon, represent a baryon. We argue that the Skyrmon can be identified as a D4-brane wrapped around $ S^4 $, which is constructed as a soliton in the world-volume gauge theory of the probe D8-branes. This wrapped D4-brane is nothing but Witten's baryon vertex, to which $ N_c $ fundamental strings are attached, and it is considered a color singlet bound state of the $ N_cThis paper presents a holographic dual 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{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 $ \eta' $ meson is also considered, and we formulate a simple derivation of the $ \eta' $ mass term satisfying the Witten-Veneziano formula from supergravity. The paper explores various aspects of massless QCD using the D4/D8 model. Among those of interest is the appearance of massless pions as the Nambu-Goldstone bosons associated with the spontaneous chiral $ U(N_f)_{L} \times U(N_f)_{R} $ symmetry breaking. In fact, we find massless pseudo-scalar mesons in the meson spectrum. We derive the low-energy effective action of the massless pions and show that it is identical to that of the Skyrme model, which consists of the chiral Lagrangian including the Skyrme term. The Skyrme term was introduced by Skyrme to stabilize the soliton solution in the non-linear sigma model. It was proposed that this soliton, called a Skyrmon, represent a baryon. We argue that the Skyrmon can be identified as a D4-brane wrapped around $ S^4 $, which is constructed as a soliton in the world-volume gauge theory of the probe D8-branes. This wrapped D4-brane is nothing but Witten's baryon vertex, to which $ N_c $ fundamental strings are attached, and it is considered a color singlet bound state of the $ N_c
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