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Baryons with Holography

Baryons with Holography. Kanabu NAWA ( RCNP ). in collaboration with. Hideo SUGANUMA ( Kyoto Univ. ). Toru KOJO ( Kyoto Univ. ). INTRODUCTION. According to the concept of ‘ holography ’ , non- perturbative aspects of QCD (meson dynamics)

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Baryons with Holography

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  1. Baryons with Holography Kanabu NAWA ( RCNP ) in collaboration with Hideo SUGANUMA ( Kyoto Univ. ) Toru KOJO ( Kyoto Univ. )

  2. INTRODUCTION According to the concept of ‘holography’, non-perturbative aspects of QCD (meson dynamics) can be analyzed by a tree-level superstring theory. Sakai-Sugimoto model : Holograhic QCD [T.Sakai and S.Sugimoto, Prog. Theor. Phys. 113, 843 (2005)] Many phenomenological aspects of mesons are uniquely derived, starting from one superstring model. Meson spectra of (axial) vector mesons. Hidden local symmetry. [Bando, et al.,1985] Vector meson dominance. [Sakurai, 1969] KSRF relation. [Kawarabayashi, Suzuki, Riazuddin, and Fayyazuddin, 1966] GSW model. [GellMann, Sharp, and Wegner, 1962]

  3. INTRODUCTION According to the concept of ‘holography’, non-perturbative aspects of QCD (meson dynamics) can be analyzed by a tree-level superstring theory. Sakai-Sugimoto model : Holograhic QCD [T.Sakai and S.Sugimoto, Prog. Theor. Phys. 113, 843 (2005)] Holographic description is reliable for large- limit. Large- QCD becomes equivalent with the weak coupling system of mesons(and glueballs); baryon does not directly appear as a dynamical degrees of freedom. [‘tHooft, Nucl. Phys. B72, 461(1974); B75, 461(1974)] How to describe a baryon in the large- holographic model ? * Chiral soliton picture . Baryon as a topological solitonin 4dim. meson effective action induced by Holographic QCD (Brane-induced Skyrmion).

  4. CONTENTS * Holography Holographic QCD * (Sakai-Sugimoto model) * Baryons in holographic QCD

  5. Gauge theory on D-branes Superstring theory has 10dim.space-time to avoid ‘anomaly’. D-brane is introduced as fixed edges of open strings. (‘D’ comes from ‘Dirichlet boundary condition’) Dp-brane = (p+1) dim. membrane open string ; scalar (NG) field. ‘perpendicular ’ ; gauge field. ‘parallel ’ (p+1) dim. gauge theory appears ‘on’ Dp-brane !!! 10dim.

  6. Holography [Maldacena (1997)] Dp-brane×Nc D-brane= black hole (black brane) [Polichinsky (1995)] 1 space dim. with finite curvature. 1 ([p+ ]+1) dim. super gravity ; low energy ; weak coupling (p+1) dim. gauge theory Strong-weak duality 10dim. ; strong coupling (S-duality)

  7. D4-brane×NC D8-brane×Nf , L 4-8 4-4 4-8 Holographic QCD [T.Sakai and S.Sugimoto, Prog. Theor. Phys. 113, 843 (2005)] Construction of massless QCD (quarks and gluons) on D4/D8/D8-branes. Index on D4 brane ( color ) Index on D8 brane ( flavor ) : quark (L) : gluon D8-brane×Nf , R 10dim. : quark (R)

  8. D4-brane×NC D8×Nf D8×Nf 10dim. space time Probe approximation with Mass of Dp-brane is proportional to its sheets number. SUGRA background D4×Nc ‘‘probe’’ D8, D8×Nf light probe light probe mNf MNC ∝ ∝ D8 heavy object gravitational background 8-8 4-8 4-4 4-8

  9. D4-brane×NC D8×Nf 4-8 4-4 D8×Nf 4-8 10dim. space time Chiral symmetry breaking and color confinement quark (L) gluon ； Chiral symmetry breaking . quark (R) L 8-8 D8 Colored particles are located behind horizon and become invisible from outside. R horizon ； Color confinement . Same critical temperature (Tc=170MeV) in lattice QCD. Mesons appear from 8-8 strings on the residual D8-branes, without explicit baryons ; property of large-Nc QCD. [‘tHooft, Nucl. Phys. B72, 461(1974); B75, 461(1974)]

  10. DBI action of probe D8-brane with D4 SUGRA background D8-brane is 9dim. membrane. ：surface tension ：dilaton field D4 SUGRA backgroud Integration out symmetric 4dims. 94 = 5 ~ 5dim. Yang-Mills theory Unified theory of mesons with pion and infinite number of (axial) vector mesons !!!

  11. 1 0 0 Mode expansion complete basis : Z Z 5dim. gauge field pion (axial) vector mesons mass : : vector Pion mainly couples with lightest vector mesons (ρ) parity : : axial-vector : vector Vector and axial-vector mesons alternately appear in the excitation spectra. : axial-vector

  12. [K. Nawa et al., Phys. Rev. D75, 086003 (2007)] 4dim. meson effective action from holographic QCD (pions and ρ-mesons) pion field : 1-form of pion field : axial vector current : , vector current : , Holographic QCD has just two parameters. pion decay constant : ρ-meson mass : All the couplings are uniquely determined !!!

  13. [K. Nawa et al., Phys. Rev. D75, 086003 (2007)] 4dim. meson effective action from holographic QCD (pions and ρ-mesons) pion field : 1-form of pion field : axial vector current : , vector current : , Traditional phenomenologies can be discussed in the action. Hidden local symmetry. [Bando, et al.,1985] Vector meson dominance. [Sakurai, 1969] KSRF relation. [Kawarabayashi et al., 1966]

  14. Comparison with phenomenology * hidden local symmetry [M. Bando, T. Kugo, and K. Yamawaki, Prog. Theor. Phys. 73, 1541 (1985); Phys. Rep. 164, 217 (1988)] Hidden local symmetric terms : , , Couplings remain as parameters. All the couplings are uniquely determined. Holographic QCD is not just the low-energy effective theory only with the constraint of symmetries in 4 dim. * chiral perturbation theory 2-derivative term L L ： 4 2 Topological picture for baryon is also supported by superstring theory. 4-derivative term ： , , Instability of Skyrmesoliton. 5dim. YM theory from holographic QCD: [I. Zahed and G.E. Brown, Phys. Rep. 142, 1 (1986)]

  15. Baryons in Holographic QCD Large- QCD becomes equivalent with the weak coupling system of mesons(and glueballs); baryon does not directly appear as a dynamical degrees of freedom. [‘tHooft, Nucl. Phys. B72, 461(1974); B75, 461(1974)] How to describe a baryon in large-Nc holographic model ? Skyrme term naturally appears ; (topological picture for baryon is also supported by superstring theory). * Baryon as a chiralsoliton [K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D75, 086003 (2007)]

  16. Hedgehog soliton with B=1 [T.H.R. Skyrme, Proc. R. Soc. A260, 127 (1961)] π; Pauli matrix ρ ; Baryon as ChiralSoliton [K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D75, 086003 (2007)] (pion) (ρ-meson) Shrinkage * Stable hedgehog soliton solution exists !!! Pions are slightly replaced by ρ-mesons through interactions in holographic QCD. * Shrinkage of pion amplitude F(r) .

  17. -meson components in the core of a Baryon (Skyrmion) (Comparison of total enegy density and each energy density in -meson channels) -mesons are actively affect the total mass of a baryon in the deeper interior of it by using various interaction channels.

  18. Mass and radius of baryon Holographic QCD has just two parameters ; ; ultraviolet cut-off scale. ;large-Nc effective theory. Experimental inputs for pion decay constant and ρ-meson mass ; MeV MeV Mass : Radius : , Exp.： (for charge radius) Isospin rotation as semi-classical quantization. Dynamical pion cloud. Increase of total size !!!

  19. Summary and outlook ‘Holography’ gives the duality between (p+1) dim. gauge theory without gravity and ([p+1]+1) dim. supergravity. S-duality gives powerful analysis for each side from the other side. S-duality makes difficult the exact proof of gauge/gravity duality. * Non-perturbative aspects of QCD : glueball mass : [E. Witten, Adv. Theor. Math. Phys. 2 (1998), 505] meson properties : [T.Sakai and S.Sugimoto, Prog. Theor. Phys. 113, 843 ; 114, 1083 (2005)] baryon properties : [K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D75, 086003 (2007)] [D.K.Hong et al. (M. Rho group),Phys. Rev. D76 : 061901 (2007)] [H. Hata et al.(Particle Theory Group, Kyoto Univ.), hep-th/0701280] * Non-perturbative aspects of gravity : critical exponent in blackhole formation : [L. Alvarez-Gaume et al., PLB 649, 478 (2007)] Hawking temperature of blackhole : [E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998)] [S. Mukherji et al., JHEP 0205 (2002) 026]

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