1 / 19

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)

mliss
Download Presentation

Baryons with Holography

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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]

More Related