Baryons and baryonic matterin holographic QCD[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D75, 086003 (2007)][K. Nawa, H. Suganuma, and T. Kojo, to be published in Phys. Rev. D79 (2009)]

Kanabu NAWA ( RCNP )in collaboration withHideo SUGANUMA ( Kyoto Univ. )Toru KOJO ( RIKEN BNL )INTRODUCTION
In 2005,
T. Sakai and S. Sugimoto succeeded in constructing massless QCD
on D4/D8/D8 multi-D brane system in type IIA superstring theory.
[T.Sakai and S.Sugimoto, Prog. Theor. Phys. 113, 843 (2005)]‘‘unified meson
theory’’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]

Classical supergravity is dual with large-Nc QCD.
As a general property of large-Nc QCD,
a baryon does not directly appear as a dynamical degrees of freedom.
[G.’tHooft, Nucl. Phys. B72, 461(1974); B75, 461(1974)]

How to describe baryons in the large-

holographic model ?

Chiral soliton picture : baryon as a soliton of meson field theory
induced by holographic QCD (‘‘brane-induced Skyrmion’’).

** Baryonic matter as a brane-induced Skyrmion on.

CONTENTS

Holographic QCD* (Sakai-Sugimoto model)
Baryonsinholographic
QCD*
Baryonicmatterinholographic
QCD*[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D75, 086003 (2007),
hep-th/0612187][K. Nawa, H. Suganuma, and T. Kojo, to be published in Phys. Rev. D79 (2009),
arXiv:0810.1005 [hep-th]]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)D4-brane×NC
D8-brane×Nf
4-8
4-4: gluon

4-8
D8-brane×Nf
10dim.

: quark (R)Probe approximation with
Mass of Dp-brane is proportional to its sheets number.

SUGRA background‘‘probe’’

D4×Nc

D8, D8×Nfcolor confinement

D4-brane×NC

8-8

D8×Nf

4-8

D84-4D8×Nf

4-8mode expansion

10dim. space timepion(axial) vector mesons

Baryon does not directly appear as a general property of[G.’tHooft, Nucl. Phys. B72, 461(1974); B75, 461(1974)]
large-Nc QCD.

Baryons in holographic QCD* chiral perturbation theory ( chiral symmetry× Lorentz invariance )L2 ：2-derivative term

4-derivative term

L4 ：

,,
Instability of Skyrme soliton.

Effective actionof D8 brane

Topological picture
for baryon is also
supported bysuperstring theory.

[I. Zahed and G.E. Brown, Phys. Rep. 142, 1 (1986)]

D8

Baryon as a chiral soliton[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D75, 086003 (2007)]

c.f. Baryon as an instanton
in 5dim. gauge theory on D8.
[D.K.Hong, M.Rho,H.-U.Yee, and P.Yi,
PRD76, 061901(2007)][H.Hata, T.Sakai, S.Sugimoto, andS. Yamato, PTP117,1157(2007)]

[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 areuniquely determined !!!

Baryon as Chiral Soliton[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D75, 086003 (2007)]

Hedgehog soliton with B=1[T.H.R. Skyrme, Proc. R. Soc. A260, 127 (1961)]

π ;
ρ ;

Pauli matrix(pion)(ρ-meson)

ShrinkageStable hedgehog soliton solution exists !!!

*Pion fields are attracted by ρ-mesons
Shrinkage of baryon.
* in the core of the baryon.

c.f. Skyrmions with HLS.
[Y.Igarashi et al., Nucl. Phys. B 259, 721 (1985)]

Strong repulsion for baryon.

Baryonic matter in holographic QCD
Baryonic matter with large Nc.

Mass :[G.’tHooft, Nucl. Phys. B72, 461(1974); B75, 461(1974)][E.Witten, Nucl. Phys. B160, 57 (1979)]

Kinetic energy :Quantum effectzero-point quantum fluctuation :[G.S.Adkins et al.,Nucl. Phys. B228, 552 (1983)]

splitting :large Nc

Static Skyrme matterSkyrmion[I.Klebanov,Nucl. Phys. B262, 133 (1985)]

One Skyrmion on S3

Static Skyrme matter‘‘ Compactification’’ of one cell

One Skyrmionon‘‘Delocalization’’ of Skyrmion

small([N.S.Manton and P.J.Ruback, Phys. Lett. B181, 137 (1986)]

large )
deconfinementchiral restoration :[A.D. Jackson et al., Nucl.
Phys.A 486, 634 (1998)].
[H.Forkel et al., Nucl.
Phys. A504, 818 (1989)]=0Total energy density of a baryon with radius[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D79 (to appear)(2009)]

Standard Skyrmion on*A baryon delocalizes
as the density increases.

*Delocalization is delayed by mesonsin the deeper interior of a baryon.

Brane-induced Skyrmion
with mesons on

Total energy density of a baryon with radius[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D79 (to appear)(2009)]

Standard Skyrmion on

Brane-induced Skyrmion
with mesons on*A baryon delocalizes
as the density increases.

All the physical quantities inholographic QCD are uniquely determinedby two experimental inputs:*Delocalization is delayed by mesonsin the deeper interior of a baryon.

Baryon number density for radius R :meson contributions in high density phase[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D79 (to appear)(2009)]

mesons tend to disappear
in high density phase !!!

R decreases.

only pions

identity mapmeson contributions in high density phase[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D79 (to appear)(2009)](conjecture)(All the (axial) vector mesons
may tend to disappear in high density phase.
1) Kinetic term suppresses the spacial distribution
for small .

2) Mass term suppresses the absolute value offor large mass.

only pions3) Couplings between pions and heavier mesons
become smaller.
[D.T.Son and M.A.Stephanov, PRD69, 065020(2004)][K. Nawa, H. Suganuma, and T. Kojo,PRD75, 086003 (2007)]

Only pions become essentialnear!!!
‘‘pion dominance’’0)

SummaryWe study baryonic matter in holographic QCD
as a brane-induced Skyrmion on .

(baryonic matter for large Nc)*

Delocalization of a baryon is delayed byin the deeper interior of it.

mesons;

Critical density forc.f.

Transition into uniform phase is somehow
related with deconfinement and/or chiral restoration.
[N.S.Manton and P.J.Ruback, Phys. Lett. B181, 137 (1986)]*mesons tend to disappear in high density phase.
conjecture

Generalization toall the (axial) vector mesons (Only pions become essential near‘‘pion dominance’’).

!!!

Chiral order parameter
Linear :Non-linear :[H.Forkel et al., Nucl.
Phys. A504, 818 (1989)]: largeLocalized order parameter[A.D. Jackson et al., Nucl.
Phys.A 486, 634 (1998)].

: largeGauge theory on D-branes
Superstring theory has 10 dim. 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‘perpendicular ’‘parallel ’

10dim.

; scalar (NG) field.
; gauge field.
(p+1) dim. gauge theory appears‘on’ Dp-brane !!!

Holography[Maldacena (1997)]

Dp-brane×Nc

D-brane = black hole (black brane)[Polichinsky (1995)]

1 space dim. with finite curvature.

([p+1 ]+1) dim. super gravity; low energy; weak coupling(p+1) dim. gauge theory
10dim.

; strong couplingStrong-weak duality(S-duality)