Skyrmions Revisited 2006Skyrmions Revisited 2006

Mannque RhoPNU & Saclay

Quarks, Nuclei and UniverseDaejon 2006

Happy Birthday !Happy Birthday ! DPM 60DPM 60

OutlineOutline

• The skyrme model with pion fields only does not work• Hidden local fields, possibly an infinite tower of them,

must be taken into account.• QCD meets string theory. New look at baryons.

Points to a new direction to nuclearPoints to a new direction to nuclearand hadronic physicsand hadronic physics

Skyrmions as QCD BaryonsSkyrmions as QCD BaryonsA history:• 1962: Skyrme: Skyrme model• 1983: Witten (Adkins, Nappi): QCD at large Nc

• 2000-2005: “Everybody” (except MR …) agrees “Skyrme model works well, say, within ~ 20%”

This is a lie. Skyrme model requires for ~20% accuracy

Then what’s OK with the Skyrme model?

• f(p)/f() ~1/2• m(p)/m() ~ 2• “Nuclei” do not at all look like nuclei

• The idea• The topological structure

• 2006: “Holographic skyrmion”: nucleon of R < 1/M2006: “Holographic skyrmion”: nucleon of R < 1/MKKKK

Pion mass crucial?Pion mass crucial?Battye and Sutcliffe 2006Battye and Sutcliffe 2006

Chiral symmetry irrelevant in nuclear physics??Chiral symmetry irrelevant in nuclear physics??

B=12B=12

Battye, Manton and Sutcliffe 2006Battye, Manton and Sutcliffe 2006

““We expect the parameters to be considerably different from those whichWe expect the parameters to be considerably different from those which emerge by fitting the proton mass, proton size and proton-delta massemerge by fitting the proton mass, proton size and proton-delta mass difference ….. for modeling nuclei.”difference ….. for modeling nuclei.”

Personal View

Since many years, it has been arguedthat vector mesons have to be includedfor a realistic description of baryons asskyrmions.

• Scoccola, Min et al: Hyperons 1989• BYPark, Min, R: pentaquark 2004

And now I am convinced more thanAnd now I am convinced more thanever the vector mesons should be there… ever the vector mesons should be there…

Sakai-Sugimoto ModelSakai-Sugimoto ModelSakai and Sugimoto 2005Sakai and Sugimoto 2005

What’s important for this talk is that baryons What’s important for this talk is that baryons mustmustemergeemerge as as IInstantonsnstantons in 5D in 5D skyrmions skyrmions in 4D in an in 4D in an tower of tower of vector mesonsvector mesons

Full story at low energy

Holographic dual skyrmion

Work in progress nowWork in progress now

• Hong, Yee, Yi, R. (HRYY)• Hata, Sakai, Sugimoto, Yamato

I shall use the general idea and map it toI shall use the general idea and map it toHarada-Yamawaki hidden local symmetryHarada-Yamawaki hidden local symmetrytheory. Then apply to the nucleon structure, e.g.theory. Then apply to the nucleon structure, e.g.nucleon form factors, vector dominance, nucleon form factors, vector dominance, the pentaquark structure … And a pseudogapthe pentaquark structure … And a pseudogapskyrmion-1/2skyrmion transitions in dense matter.skyrmion-1/2skyrmion transitions in dense matter.

Holographic dual skyrmion predictsHolographic dual skyrmion predicts::

The 5D instanton size is tiny R< 1/mN. This means that in 4D the infinite tower of vector mesons shrink the skyrmion from R ~ 0.6 to R ~ 0.2 fm. Therefore the nucleon EM form factor must be largely vector dominated.

This explains the long-standing puzzle why the nucleon form factors cannot be understood with VD by the lowest and while the VD works well for the pion form factor. Enter Harada-Yamawaki HLS theory …

This works fine for the JLab resultThis works fine for the JLab result

The Jlab can be fit with VD by ’, …, , ’

Violation of VD in HY’s HLSViolation of VD in HY’s HLSHarada and Yamawaki 2001Harada and Yamawaki 2001

HY’s HLS theory can be viewed as HLS with an infiniteHY’s HLS theory can be viewed as HLS with an infinitetower with all vector mesons other than the lowest onestower with all vector mesons other than the lowest onesIntegrated outIntegrated out and then and then matchedmatched to QCD correlators at to QCD correlators at the matching scale the matching scale

EM currentEM current

pp pp

Mocks up “Tower”Mocks up “Tower”

Harada and Yamawaki found the “vector manifestation”Harada and Yamawaki found the “vector manifestation”(VM) fixed point ((VM) fixed point (a, ga, g)=()=(1, 01, 0) and Nature tends to flow away) and Nature tends to flow awayfrom from a=2a=2 at which VD holds. The VD with at which VD holds. The VD with aa==22 is an is an ““accident”. E.g., accident”. E.g., matter in matter in heat bathheat bath or in or in densitydensity tends to tends to move to move to a=1.a=1. In some sense In some sense a a “knows” about the tower.“knows” about the tower.

Proton favors Proton favors a a 1 1 Known since a long time!!Known since a long time!!

• Iachello, Jackson and Lande 1973Iachello, Jackson and Lande 1973 ½½ and and ½ ½ modelmodel• Brown, Rho and Weise 1986Brown, Rho and Weise 1986 Chiral bag at magic angle Chiral bag at magic angle //22• Bijker 2005Bijker 2005 Multi-parameter fitMulti-parameter fit

BijkerBijker

Iachello et alIachello et al

Physics with Physics with a a 11The nucleon and nuclear structure favor The nucleon and nuclear structure favor aa near 1. near 1.Holographic skyrmion says it’s natural. Holographic skyrmion says it’s natural. This means that the This means that the everybodyeverybody in the tower plays in the tower playsan important role in the baryon sector.an important role in the baryon sector.

This has a remarkable ramification on the structureThis has a remarkable ramification on the structureof the of the + + pentaquark, never mind whether it is seenpentaquark, never mind whether it is seenin experiments or not. in experiments or not.

We use 2 characteristics of skyrmions with vector mesons:We use 2 characteristics of skyrmions with vector mesons:(1) (1) TopologyTopology and (2) and (2) aa is near is near 11 in baryonic environment. in baryonic environment.

Pentaquark as a bound KPentaquark as a bound K++-skyrmion-skyrmion

String theorists Klebanov, Itzhaki et al argued that theString theorists Klebanov, Itzhaki et al argued that thebound Kbound K++- soliton picture is consistent with large N- soliton picture is consistent with large Nc c and theand thechiral limit. I agree.chiral limit. I agree.

In fact in 1988, Scoccola, Min et al argued for the bound-stateIn fact in 1988, Scoccola, Min et al argued for the bound-statemodel but with the vector mesons model but with the vector mesons and and ..

In 2004, BYPark, Min and R. applied to the pentaquark problemIn 2004, BYPark, Min and R. applied to the pentaquark problemthe same Lagrangian as that of Scoccola et al which is just the same Lagrangian as that of Scoccola et al which is just HY’s hidden local symmetry Lagrangian, with one HY’s hidden local symmetry Lagrangian, with one elementelementwhich made the calculation which made the calculation incompleteincomplete, which makes the, which makes theresult untrustworthy and the outcome inconclusive.result untrustworthy and the outcome inconclusive.

Park, Min, R. 2004Park, Min, R. 2004

However the qualitative result is most likely valid becauseHowever the qualitative result is most likely valid becauseit has to do with the importance of the infinite tower ofit has to do with the importance of the infinite tower ofvector mesons.vector mesons.

What was wrong in BYPark et al?What was wrong in BYPark et al?

The holographic dual QCD dictates that The holographic dual QCD dictates that LLanomalousanomalous is completely is completelyvector dominated. In terms of HY’s HLS, this means that vector dominated. In terms of HY’s HLS, this means that the the 33 does does notnot have the direct coupling , have the direct coupling ,

00

This means that some of the coefficients that appear inThis means that some of the coefficients that appear inthe “induced” WZ terms used by Park et al are not the “induced” WZ terms used by Park et al are not consistent with HY’s HLS.consistent with HY’s HLS.

This “correction work” has not been done; one of the termsThis “correction work” has not been done; one of the termsappears to be very arduous though straightforward…appears to be very arduous though straightforward…

This (I believe) does not disturb the qualitative structure of theThis (I believe) does not disturb the qualitative structure of thetheory. theory.

In short, what must happen is the followingIn short, what must happen is the following

KK++ binds to the skyrmion in the infinite tower of the vector binds to the skyrmion in the infinite tower of the vectormesons. The latter is approximated in HY’s HLS theory mesons. The latter is approximated in HY’s HLS theory (i.e., in Scoccola et al’s Lagrangian) by (i.e., in Scoccola et al’s Lagrangian) by a a 1 1

Roughly, the infinite tower corresponds toRoughly, the infinite tower corresponds to a ~ 4/3a ~ 4/3

a = 4/3a = 4/3

Skyrmion-1/2 skyrmion transitionSkyrmion-1/2 skyrmion transition

Topology is most probably the same for the Skyrme solitonTopology is most probably the same for the Skyrme soliton and and holographic skyrmion. Topology is robust (e.g., quantumholographic skyrmion. Topology is robust (e.g., quantumcomputers (a la Sarma et al ) are being built on topology)computers (a la Sarma et al ) are being built on topology)

Assume that topology is preserved when skyrmions are put Assume that topology is preserved when skyrmions are put on crystals.on crystals.

Study of topology of skyrmions on crystal: Work by BYPark,Study of topology of skyrmions on crystal: Work by BYPark,Min, H.J. Lee, Vento, R. at KIAS 1999-2004Min, H.J. Lee, Vento, R. at KIAS 1999-2004

Found:Found:Phase transition from skyrmions to half-skyrmionsPhase transition from skyrmions to half-skyrmionsat some density, identified as at some density, identified as chiral transitionchiral transition

SkyrmionSkyrmion

U=exp (i2U=exp (i2/f/f))

Half skyrmionHalf skyrmion

U=U=LL++

Pseudo-gapPseudo-gap phasephase

““deconfine”deconfine”

HLS (emergent) gauge fieldHLS (emergent) gauge field

sfisfiRL

RLRLfi

ee

xhxheU2/2/

)(

/ )()(

SU(NF) local gauge theory with SU(NF)

)()(

)( ,,

F

RLRL

NSUxh

xh

Invariance

This is hidden local symmetry theory of Harada and Yamawaki

Vector mesons Vector mesons emerge as hidden gauge bosons;emerge as hidden gauge bosons;Back with Harada and Yamawaki again.Back with Harada and Yamawaki again.

Redundant field to be eaten upto make the massive

BR scaling

An analogy tocondensed matter

Perhaps a generic feature inAll strongly correlated matter ?

Phase change takes place through deconfinement of a skyrmion into 2 half-skyrmions at the boundary.The ½-skyrmions are confinedto each other in both phasesby hedgehog gauge field (HGF).Deconfinement occurs whenHGF is “decoupled”.

A: magnetic Néel ground state Sigma model

B: VBS quantum paramagnet

Senthil et al, Nature 303 (2004) 1490

Sigma model

)1()()(

Uxh zxhz

z zn

Invariance:

Local gauge symmetrywith U(1) gauge field A

CP1 parameterization Hidden gauge symmetry

2422

2

)(|||||)(|

AzuzsziAL

L rddS

n nn rdQ yx2

41

)(2xyyx AArd ~

Topological charge (skyrmion number) Q

z = fractional spinon =1/2- skyrmion = “meron”

1/2-skyrmions are confined by topologyAt the phase transition, the “monopole” (topology) becomes irrelevantand the 1/2-skyrmions get deconfined, the integer skyrmion numberbecoming non-conserved.

Senthil et al’s “deconfined quantum critical points”

1/2- skyrmion

Deconfined up-meron-down-antimeron

““skyrmion”skyrmion”

““half-skyrmion”half-skyrmion”““skyrmion”skyrmion”superqualitonsuperqualiton

The future looks great for theThe future looks great for theNext generation in this field!!Next generation in this field!!