Hadronic matter Hadronic matter from the vector from the vector manifestation manifestation

(VM) fixed point(VM) fixed pointMannque RhoMannque Rho

Chiral 05/RIKENChiral 05/RIKEN

OutlineOutline

Physics around the VM fixed pointPhysics around the VM fixed point Question of scalesQuestion of scales Need for, and power of, HLS (hidden Need for, and power of, HLS (hidden

local symmetry) for vector mesonslocal symmetry) for vector mesons VD (vector dominance) is VD (vector dominance) is generically generically

maximally violated maximally violated in naturein nature Predictions: (1) Predictions: (1) MM**

near chiral near chiral restoration, (2)restoration, (2) Pentaquark, (3) Pentaquark, (3) “strange nugget” out of a neutron star“strange nugget” out of a neutron star

HLS : HLS : two points where two points where theory theory

is precisely knownis precisely known

VM

VAC

VM

Propose:Fluctuate around VMInstead of around VAC

Scales (hadrons)Scales (hadrons)

E << E << mm ::

E ~ E ~ mm::

•“Ultraviolet complete” to QCD• Baryons must arise as skyrmions

Scales (nuclei)Scales (nuclei)

E << E << mm

EEmm

EEmmTower of vector mesons figure.

Physics with or without vector mesons can be drastically different

Case: Pion velocity vCase: Pion velocity v near Tnear Tcc

Linear Linear model (with no vector mesons): model (with no vector mesons): vv= 0 = 0 ((Son and Stephanov Son and Stephanov

2002)2002)

Hidden local symmetry (with vector Hidden local symmetry (with vector

mesons)mesons) vv 1 1 ((Harada, Rho and Sasaki Harada, Rho and Sasaki

2004)2004)Caveat: Lorentz symmetry breaking leads to a small deviation from the velocity of light

Vector mesons with or without local gauge invariance can lead to drastically different physics

Case: Vector meson mass at Case: Vector meson mass at TTcc

Without gauge invariance, with vector dominance Without gauge invariance, with vector dominance (VD):(VD):

mmcc)/)/mmPisarski 1998Pisarski 1998

With hidden gauge invariance, hence VD With hidden gauge invariance, hence VD maximallymaximally

violated:violated:

mmcc)/)/mmHarada, Yamawaki 2001-Harada, Yamawaki 2001-20022002

Harada, Sasaki 2002Harada, Sasaki 2002 (Brown, Rho 1991)(Brown, Rho 1991)

Desperately looking for guidance

• No guidance from QCD gauge theory proper, so groping in the darkness gives the quagmire!!!• But string theory AdS/QCD hidden local symmetry!

Why need local gauge Why need local gauge symmetry for the vector symmetry for the vector

mesons?mesons?

Consider physics of the EFT given by

Massive Yang-Mills Lagrangian with mass mA=g2 f valid at low energy: But there is no gauge invarianceIf one wants to go to a higher energy scale, say, 4f, then one is at a loss with no symmetry guidance:

+ many other terms “Quagmire” results

I.e.

Solution

•Introduce Goldstone bosons U=exp (i/f) and an additional gauge field A1 •Write gauge-invariant Lagrangian involving A2, A1 and U

• Gauge fix : U =1 or =0• Let g1=0, decoupling A1

Gauge invariant

Unitary gauge

“Hidden gauge invariance” with the field eatenup to give the mass to A2 : Higgsing

What’s gained

+ “quagmire”

•Book-keeping order by order (e.g., ChPT)•Valid to the scale 4f beyond which “ultraviolet completed” to a fundamental theory•No problem handling mA 0. Important for later!

Hidden Local Symmetry Hidden Local Symmetry (HLS) (HLS)

a la Harada-Yamawakia la Harada-Yamawaki

• Pick the matching scale: M =4fGeV• Pick relevant degrees of freedom below M : SU( Nf ), ignore scalars (can be put in if needed), integrate out a1 , glueballs etc. Baryons emerge as skyrmions• Pick relevant degrees of freedom above M : quark , G

• Ultraviolet complete by Wilsonian matching at M

• Quantize at loop orders : RGE

Harada and Yamawaki Phys. Rept. 381 (2003) 1- 233

Identify with HY fields: L† =L , R =R

Note:a=1 “Theory-space locality”

HY Lagrangian

“Open moose”

(De)Constructing 5(De)Constructing 5thth DimensionDimension

Let 0 , put nearest-neighbor vectors Ak

connected by link fields k Tower of vectors

21

1

2

1

22 ||)( k

N

kk

N

kk DrTfFTrg L

Generalize open moose

5-D gauge theory with 5th-D on lattice!!

Let N ∞ and go to continuum

Pure Yang-Mills + Chern-Simonsin curved space in five-D

To do QCD, put ultraviolet and infrared cutoffs in the fifth D

Son and Stephanov 2004Others …

xAdxU (55

fixxAdxiePe 2/),(

~555With

What’s the big deal?

•Tower of hidden local symmetry gives5-D (YM) gauge theory•String theory gives the same 5-D gauge theory which is dual to QCDon the 4-D surface !

Glashow explained that the Albert Einstein, who failed in his search to find a unified theory of forces in the universe, spent the last three decades of his life isolated from the scientific community.

"It is tragic," Glashow said, "but now, we have the string theorists, thousands of them, that also dream of explaining all the features of nature. They just celebrated the 20th anniversary of superstring theory.

"So when one person spends 30 years, it's a waste, but when thousands waste 20 years in modern day, they celebrate with champagne. I find that curious."

Glashow on string theory

String theory HLSString theory HLS Maldacena 97: AdS/CFT duality Maldacena 97: AdS/CFT duality Karch, Katz, Witten, Klebanov, Strassler … : Karch, Katz, Witten, Klebanov, Strassler … :

Deform geometry in the dual gravity sector, Deform geometry in the dual gravity sector, introduce quark flavor D branes as probes introduce quark flavor D branes as probes and construct gravity theory in the bulk and construct gravity theory in the bulk (5D) dual to a gauge theory on the surface (5D) dual to a gauge theory on the surface (4D) (4D)

Sakai, Sugimoto 04: Succeeded to construct Sakai, Sugimoto 04: Succeeded to construct a bulk theory in 5-D a bulk theory in 5-D dualdual to QCD on 4-D to QCD on 4-D surface with surface with correct correct chiral symmetry chiral symmetry breaking. breaking.

Upshot

• 5-D YM theory in the bulk leads (via holography) to 4-D HLS of a tower of vector mesons: the parameters of the theory fixed by the bulk constants • Confined to the lowest member of thetower, , it leads to HY theory!

Therefore

HLS with is “dual” to QCD

Baryons must arise as skyrmions inHLS theory

Vector manifestation Vector manifestation in the chiral limitin the chiral limit

C. Sasaki’s TalkHLS matched to QCD at M

Flows to the “VM fixed point”

g 0f 0

a 1(0)

As (T, n, Nf ) (Tc , nc , Nf c)

The vector meson mass vanishesnear the critical point

mV ~ a1/2 Fg ~ <qq>+ …

And a ~ 1.

Quark mass corrections

Consequence

V/mV ~ <qq> + …

FalsifiablePrediction

Physics Around VM

HLS is well defined at the VM so if nature is not too far from the VM, why not start from there?

HY showed that both g and f depart from 0 but a stays~ 1 (or ~ 0), i.e., “theory-space local”.

Vector Dominance

L=-2eag F2 ATr [Q] +2i (1-a/2)ATr [VQ]

a=2 : VD a=1 : maximal violation of VD

Evidences that Evidences that a~1a~1

EM pion mass differenceEM pion mass difference ““Dynamical origin of Little Higgs” (Harada, Yamawaki 03)Dynamical origin of Little Higgs” (Harada, Yamawaki 03) Chiral doubling of heavy-light hadronsChiral doubling of heavy-light hadrons (Harada, Rho, Sasaki (Harada, Rho, Sasaki

04)04)

Nucleon form factors: Violation of VDNucleon form factors: Violation of VD (Iachello, Jackson, Lande 73, Brown, Rho, Weise (Iachello, Jackson, Lande 73, Brown, Rho, Weise

86)86)

Matter in heat bath: Violation of VDMatter in heat bath: Violation of VD (Harada, Sasaki 04) (Harada, Sasaki 04)

Prediction 1Prediction 1 Parametric massParametric mass of of all light-quark all light-quark

hadronshadrons MM scales in medium near VM as scales in medium near VM as

MM**/M /M ≈ ≈ ((<qq><qq>**/<qq>/<qq>))nn +…+ +…+ O O (m(mquarkquark))

• The The and and (parametric and pole) masses: (parametric and pole) masses: mmmm0 with the width going to zero more 0 with the width going to zero more quickly. quickly. (Explicit (Explicit SB will smear the sharp SB will smear the sharp predictions.)predictions.)• The D-meson chiral splitting will go to zero The D-meson chiral splitting will go to zero modulo modulo quark-mass corrections .quark-mass corrections .• Etc. etc.Etc. etc.

Prediction 2Prediction 2

• Since HLS is dual to QCD, baryons must come as skyrmions• The celebrated DPP (rigid rotor) skyrmion is not consistent with large Nc.

• The bound kaon-soliton skyrmion for S=±1 is consistent with large Nc.

But there is no bound S=+1 without HLS without HLS Itzahki et al 2004).• With HLS, Vector mesons are very (not) important for S>0 (<0) baryons. K+ (K- ) binding is very sensitive (insensitive) to a (or ) which acts as a “magnetic field”

K K ++ will be bound to will be bound to sskyrmion to produce pentaquark

- skyrmion complex

Bound for a < 1.3 Unbound for a > 1.3AdS/QCD gives “a” ~ 1.3 HLS/VM gives a 1- 1.3

~Large Nc

Therefore for large Nc , K+ is bound to skyrmion

~

Physics of bound Physics of bound (Park, Rho, Min 04)

Prediction 3Prediction 3

Brown, Lee, Rho 05

Scoop a nugget containing 2 neutrons, 1 proton and 1 K- out of a neutron star on the way to a blackhole with kaon condensed at n 3.1 n0 (Thorsson,Prakash, Lattimer 94). Here on the average one electron is replaced by a K-

Strange nugget of a neutron star

S0 (3115): nnpK- ? In progress

Fluctuating around VM