Deconfined HalfSkyrmion Matter at High Density

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Deconfined Half-Skyrmion Matter at High Density
NFQCD08 Kyoto

• Quantum critical phenomenon

Mannque Rho IPhT, CEA Saclay
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Proposal

• DDC hQCD ? Non-perturbative strong interaction
  phenomena at E ltlt L can be encapsulated in 5D YM
  Chern-Simons action.

SCS
? Quenched approximation

• In 4D, S describes Goldstone pions coupled to an
  
• Infinite tower of hidden local gauge fields.

HLS?

• Integrate out the tower and retain only the g.s.
• vector mesons r, w, f.

HLS1
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Conclusion
Hadron-quark continuity via ½-skyrmions
Park, Vento, R. 2001
Hong, R., Zahed 1999
½ skyrmions
CFL
hadronic
Baryonic Matter
squaliton
skyrmion

m
Non-Fermi liquid
HLS1
Applicable in both sectors
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Baryons are peculiar
String theory
Wittens baryon vertex (wrapped D4 on S4)
dissolves into D8 branes in the Sakai-Sugimoto
model
D4
D8
Nc
D8
Therefore baryons must appear in 5D YM theory as
instantons
or In 4D as skyrmions embedded in infinite tower
of vector mesons
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hQCD Predictions

• Complete vector dominance of the form factors
  for p, r, w, , N with the infinite tower emerges
  from 5D YM CS.
• Solitonic baryon structure drastically different
  from that of the standard skyrmion model without
  vector mesons new structure for nuclei
• Dense matter is qualitatively different from the
  conventional structure

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VD for Baryon
There is a point-like instanton configuration
? Expect
rk

The instanton merges into the tower which takes
over whole picture.
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Presents
A totally new perspective on topological
structure of baryons and dense baryonic matter

• BR scaling
• Kaon condensation
• Skymion-half-skyrmion transition
• 4. CFL
• 5. Compact star structure
• Etc.

• This talk

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Work with HLS1
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HLS1 a la Harada-Yamawaki
Harada and Yamawaki 2001

• HLS1 Lagrangian in the chiral limit 3
  parameters
• g (gauge coupling), Fp and Fs or (g, Fp , a
  (Fs/Fp)2)

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Vector Manifestation at High Density
Harada, Kim, R 2003
As n? nc,
Robust in the chiral limit
Require a gauge-invariant treatment!! Not
available in medium.
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Poor mans approach to HLS1

• Gauge fix to unitary gauge

• Simulate the dropping mass by dilaton ltcgt
• via the trace anomaly
• Implement the dropping gauge coupling

Brown, R. 1991
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Model
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Anomaly term
Scale invariant as is. In medium, vector
manifestation requires that the gauge coupling
drop. To implement this, multiply this term
by cn. This will develop a mean field (ltcgt)n.
We find n2, 3 work. So pick n3. Caveat ad
hoc!!
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Method
Park, Vento, R (04, 08)

• Put on crystal lattice a la Klebanov
  (1985), Kugler
• and Shtrikman (1988) and others and squeeze
  the
• crystal.
• Energetically favored is the FCC employed by KS.
  
• Generalize to include c, r w.

• Symmetry consideration shows that at some high
  density
• the skyrmion fractionizes into half-skyrmions in
  BCC as
• first shown in the Skyrme model by Goldhaber and
• Manton (1987).

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Skyrme Model
Without c, r, w
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Predicted phase diagram
With c, r w
fpfs ? a1
Georgis vector mode
density n
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Striking results
Crucially dependent on the dilaton mass
Single baryon

• For mc lt 1 GeV, Msol 0.95 GeV and R 0.1fm
• For mc gt 1 GeV, Msol 1.4 GeV and R 0.5fm

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Dense matter
fp
mc 720 MeV
mc 3000 MeV
1
1
fp
1/2
1/2
half-skyrmion/ pseudogap phase
0
0
1
1
2
2
LF
LF
Half-skyrmion phase shrinks
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Anomaly-induced quark-hadron continuity
Yamamoto, Hatsuda, Tachibana, Baym 2007
Leakage through the gate
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Hadron-to-CFL as Skyrmion-to-Squaliton

• Baryonic matter is a skyrmion matter
• CFL matter is a quark skyrmion (squaliton)
  matter
• Skyrmion to squaliton goes through half-skyrmion
• matter

½ skyrmions
CFL
hadronic
squaliton
skyrmion

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Analogy to Condensed matter?
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Deconfined quantum critical phenomenon
Senthil et al, Nature 303 (2004) 1490
Magnetic Néel ground state
Via ½ skyrmions
V(alence)B(ond)S(olid) paramagnet
A?B second order phase transition without order
parameter. It goes through deconfined
half-skyrmion phase. Does not belong to
Ginzburg-Landau-Wilson class
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Sigma model
spinon
CP1 parameterization
Invariance
Emergent/hidden local gauge symmetry
U(1) gauge field Am
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O(3) nonlinear sigma model for the Néel
phase
Order parameter
Berry phase
Non-trivial topology with hedgehog
skyrmion
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z fractional spinon 1/2- skyrmion
meron
1/2-skyrmions are confined/deconfined by topology
At the phase transition, the monopole
(topology) becomes irrelevant and the
1/2-skyrmions get deconfined. This is manifest
via the gauge field.
Senthil et als deconfined quantum critical
point
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Deconfined up-meron-down-antimeron
1/2- skyrmion
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Back-Up
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Model
Mode expansion
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LF fm)