Baryons with Holography
description
Transcript of Baryons with Holography
Baryons with Holography
Hideo SUGANUMA ( Kyoto Univ. )Toru KOJO ( Kyoto Univ. )
Kanabu NAWA ( RCNP )in collaboration with
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)]
INTRODUCTION
Meson spectra of (axial) vector mesons.Hidden local symmetry.Vector meson dominance.KSRF relation.GSW model.
[Bando, et al.,1985]
[Sakurai, 1969]
[Kawarabayashi, Suzuki, Riazuddin, and Fayyazuddin, 1966]
[GellMann, Sharp, and Wegner, 1962]
Many phenomenological aspects of mesons are uniquely derived, starting from one superstring model.
INTRODUCTION
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.
How to describe a baryon in the large- holographic model ?
*Chiral soliton picture .Baryon as a topological soliton in 4dim. meson effective actioninduced by Holographic QCD (Brane-induced Skyrmion).
[‘tHooft, Nucl. Phys. B72, 461(1974); B75, 461(1974)]
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)]
Holography
Holographic QCD (Sakai-Sugimoto model)
Baryons in holographic QCD***
CONTENTS
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
‘parallel ’
‘perpendicular ’ ; scalar (NG) field.
; gauge field.
(p+1) dim. gauge theory appears‘on’ Dp-brane !!!
10dim.
Holography
10dim.
Dp-brane×Nc
1 space dim. with finite curvature.
(p+1) dim. gauge theory
([p+ ]+1) dim. super gravity1
; low energy; weak coupling
; strong couplingStrong-weak duality
(S-duality)
D-brane = black hole (black brane)[Polichinsky (1995)]
[Maldacena (1997)]
Holographic QCD
Construction of massless QCD (quarks and gluons)
on D4/D8/D8-branes.
[T.Sakai and S.Sugimoto, Prog. Theor. Phys. 113, 843 (2005)]
D4-brane×NC
D8-brane×Nf , L
4-4
4-8
4-8D8-brane×Nf , R
Index on D4 brane ( color )Index on D8 brane ( flavor )
: quark (L)
: quark (R)
: gluon
10dim.
Probe approximation with
Mass of Dp-brane is proportional to its sheets number.
D4×NcD8, D8×Nf ‘‘probe’’
SUGRA background
light probe
heavy object
gravitational background
m Nf∝
D4-brane×NC
D8×Nf
D8×Nf
10dim. space time
D8
light probe
4-4
4-8
4-8
8-8
M NC∝
[‘tHooft, Nucl. Phys. B72, 461(1974); B75, 461(1974)]
D4-brane×NC
D8×Nf
D8×Nf
4-4
4-8
4-8
Chiral symmetry breaking and color confinement
10dim. space time
; Chiral symmetry breaking .
Colored particles are located behind horizonand become invisible from outside.
quark (L)
quark (R)
gluon
8-8
D8
horizon
L
R; 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.
~
DBI action of probe D8-brane with D4 SUGRA background
: surface tension
9 4 = 5
5dim. Yang-Mills theory
D8-brane is 9dim. membrane.
: dilaton fieldD4 SUGRA backgroud
Integration out symmetric 4dims.
Unified theory of mesons with pion and infinite number of (axial) vector mesons !!!
00
1
Mode expansion
: vector
: vector
: axial-vector
mass :parity :
Z Z
pion (axial) vector mesons
: axial-vector
complete basis :
5dim. gauge field
Pion mainly coupleswith lightest vector mesons (ρ)
Vector and axial-vector mesonsalternately appear in the excitation spectra.
(pions and ρ-mesons)
4dim. meson effective action from holographic QCD
,
,
pion field :
1-form of pion field :
axial vector current :
vector current :
pion decay constant :
ρ-meson mass :
Holographic QCD hasjust two parameters.
All the couplings are uniquely determined !!!
[K. Nawa et al., Phys. Rev. D75, 086003 (2007)]
(pions and ρ-mesons)
4dim. meson effective action from holographic QCD
,
,
pion field :
1-form of pion field :
axial vector current :
vector current :
Traditional phenomenologiescan be discussed in the action.
Hidden local symmetry.
Vector meson dominance.
KSRF relation.
[Bando, et al.,1985]
[Sakurai, 1969]
[Kawarabayashi et al., 1966]
[K. Nawa et al., Phys. Rev. D75, 086003 (2007)]
hidden local symmetry* [M. Bando, T. Kugo, and K. Yamawaki, Prog. Theor. Phys. 73, 1541 (1985); Phys. Rep. 164, 217 (1988)]
Comparison with phenomenology
Hidden local symmetric terms :
Couplings remain as parameters. All the couplings are uniquely determined.
Holographic QCD is not just the low-energy effective theoryonly with the constraint of symmetries in 4 dim.
chiral perturbation theory*:
: ,,
[I. Zahed and G.E. Brown, Phys. Rep. 142, 1 (1986)]
2-derivative term
4-derivative term
Instability of Skyrme soliton.5dim. YM theoryfrom holographic QCD:
Topological picturefor baryon is also supported bysuperstring theory.
L2
L4
,,
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 chiral soliton[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D75, 086003 (2007)]
Baryon as Chiral Soliton
[T.H.R. Skyrme, Proc. R. Soc. A260, 127 (1961)]
π ;ρ ;
Pauli matrix
Hedgehog soliton with B=1
Shrinkage
Pions are slightly replaced by ρ-mesons through interactionsin holographic QCD. Shrinkage of pion amplitude F(r) .
Stable hedgehog soliton solution exists !!!**
(pion) (ρ-meson)
[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D75, 086003 (2007)]
-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 baryonin the deeper interior of itby using various interaction channels.
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 ;
Mass : ,
MeV MeV
Exp. :
Radius :
Isospin rotation as semi-classical quantization.
Dynamical pion cloud.
Increase of total size !!!
(for charge radius)
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 :
baryon properties :
meson properties :
Non-perturbative aspects of gravity :critical exponent in blackhole formation :Hawking temperature of blackhole :
*
*
[E. Witten, Adv. Theor. Math. Phys. 2 (1998), 505]
[T.Sakai and S.Sugimoto, Prog. Theor. Phys. 113, 843 ; 114, 1083 (2005)]
[K. Nawa, H. Suganuma, and T. Kojo, Phys. Rev. D75, 086003 (2007)]
[L. Alvarez-Gaume et al., PLB 649, 478 (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]
[S. Mukherji et al., JHEP 0205 (2002) 026][E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998)]