Skyrmions Revisited 2006

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Skyrmions Revisited 2006

• Mannque Rho
• PNU Saclay

Quarks, Nuclei and Universe Daejon 2006
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Happy Birthday ! DPM 60
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Outline

• 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 nuclear and hadronic
physics
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Skyrmions as QCD Baryons
A 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

• fp (p)/fp(p) 1/2
• mp(p)/mp(p) 2
• Nuclei do not at all look like nuclei

Then whats OK with the Skyrme model?

• The idea
• The topological structure

• 2006 Holographic skyrmion nucleon of R lt
  1/MKK

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Pion mass crucial?
Battye and Sutcliffe 2006
Chiral symmetry irrelevant in nuclear physics??
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Battye, Manton and Sutcliffe 2006
B12
We expect the parameters to be considerably
different from those which emerge by fitting the
proton mass, proton size and proton-delta mass
difference .. for modeling nuclei.
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Personal View
Since many years, it has been argued that vector
mesons have to be included for a realistic
description of baryons as skyrmions.

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

And now I am convinced more than ever the vector
mesons should be there
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Sakai-Sugimoto Model
Sakai and Sugimoto 2005
Full story at low energy
?
Whats important for this talk is that baryons
must emerge as
Instantons in 5D ? skyrmions in 4D in an ? tower
of vector mesons
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Holographic dual skyrmion
Work in progress now

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

I shall use the general idea and map it
to Harada-Yamawaki hidden local symmetry theory.
Then apply to the nucleon structure, e.g. nucleon
form factors, vector dominance, the pentaquark
structure And a pseudogap skyrmion-1/2skyrmion
transitions in dense matter.
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Holographic dual skyrmion predicts
The 5D instanton size is tiny Rlt 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 works fine for the JLab result
The Jlab can be fit with VD by r, r, , w, w,
...
This explains the long-standing puzzle why the
nucleon form factors cannot be understood with VD
by the lowest r and w while the VD works well for
the pion form factor. Enter Harada-Yamawaki HLS
theory
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Violation of VD in HYs HLS
Harada and Yamawaki 2001
HYs HLS theory can be viewed as HLS with an
infinite tower with all vector mesons other than
the lowest ones Integrated out and then matched
to QCD correlators at the matching scale
EM current
g
g
r, w
p
p
Mocks up Tower
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Harada and Yamawaki found the vector
manifestation (VM) fixed point (a, g)(1, 0) and
Nature tends to flow away from a2 at which VD
holds. The VD with a2 is an accident. E.g.,
matter in heat bath or in density tends to move
to a1. In some sense a knows about the tower.
Proton favors a ? 1
Known since a long time!!

• Iachello, Jackson and Lande 1973
• ½ and ½ model
• Brown, Rho and Weise 1986
• Chiral bag at magic angle qp/2
• Bijker 2005
• Multi-parameter fit

Bijker
Iachello et al
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Physics with a ? 1
The nucleon and nuclear structure favor a near
1. Holographic skyrmion says its natural. This
means that the everybody in the tower plays an
important role in the baryon sector. This has a
remarkable ramification on the structure of the
Q pentaquark, never mind whether it is seen in
experiments or not.
We use 2 characteristics of skyrmions with vector
mesons (1) Topology and (2) a is near 1 in
baryonic environment.
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Pentaquark as a bound K-skyrmion
Park, Min, R. 2004
String theorists Klebanov, Itzhaki et al argued
that the bound K- soliton picture is consistent
with large Nc and the chiral limit. I agree. In
fact in 1988, Scoccola, Min et al argued for the
bound-state model but with the vector mesons r
and w. In 2004, BYPark, Min and R. applied to
the pentaquark problem the same Lagrangian as
that of Scoccola et al which is just HYs hidden
local symmetry Lagrangian, with one element which
made the calculation incomplete, which makes
the result untrustworthy and the outcome
inconclusive.
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However the qualitative result is most likely
valid because it has to do with the importance of
the infinite tower of vector mesons. What was
wrong in BYPark et al? The holographic dual QCD
dictates that Lanomalous is completely vector
dominated. In terms of HYs HLS, this means that
the w ? 3p does not have the direct coupling ,
p
w
? 0
p
p
This means that some of the coefficients that
appear in the induced WZ terms used by Park et
al are not consistent with HYs HLS.
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This correction work has not been done one of
the terms appears to be very arduous though
straightforward This (I believe) does not
disturb the qualitative structure of the theory.
In short, what must happen is the following K
binds to the skyrmion in the infinite tower of
the vector mesons. The latter is approximated in
HYs HLS theory (i.e., in Scoccola et als
Lagrangian) by a ? 1
Roughly, the infinite tower corresponds to a
4/3
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a 4/3
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Skyrmion-1/2 skyrmion transition
Topology is most probably the same for the Skyrme
soliton and holographic skyrmion. Topology is
robust (e.g., quantum computers (a la Sarma et al
) are being built on topology) Assume that
topology is preserved when skyrmions are put on
crystals. Study of topology of skyrmions on
crystal Work by BYPark, Min, H.J. Lee, Vento, R.
at KIAS 1999-2004
Found Phase transition from skyrmions to
half-skyrmions at some density, identified as
chiral transition
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Skyrmion
Uexp (i2p/fp)
deconfine
Half skyrmion
UxLxR
Pseudo-gap phase
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HLS (emergent) gauge field
Vector mesons rmemerge as hidden gauge
bosons Back with Harada and Yamawaki again.
Redundant field to be eaten up to make the r
massive
Invariance
SU(NF) local gauge theory with rm ? SU(NF)
This is hidden local symmetry theory of Harada
and Yamawaki
BR scaling
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An analogy to condensed matter
Perhaps a generic feature in All strongly
correlated matter ?
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A magnetic Néel ground state Sigma
model
B VBS quantum paramagnet
Phase change takes place through deconfinement
of a skyrmion into 2 half-skyrmions at the
boundary. The ½-skyrmions are confined to each
other in both phases by hedgehog gauge field
(HGF). Deconfinement occurs when HGF is
decoupled.
Senthil et al, Nature 303 (2004) 1490
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Sigma model
CP1 parameterization
Hidden gauge symmetry
Invariance
Local gauge symmetry with U(1) gauge field Am
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z fractional spinon 1/2- skyrmion
meron
Topological charge (skyrmion number) Q
?
1/2-skyrmions are confined by topology
At the phase transition, the monopole
(topology) becomes irrelevant and the
1/2-skyrmions get deconfined, the integer
skyrmion number becoming non-conserved.
Senthil et als deconfined quantum critical
points
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Deconfined up-meron-down-antimeron
1/2- skyrmion
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skyrmion
skyrmion superqualiton
half-skyrmion
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The future looks great for the Next generation in
this field!!