BRscaling in AdSQCD

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• BR-scaling in AdS/QCD

Sang-Jin Sin (Hanyang Univ.) 2007.10.20
_at_KIAS Based on work with Seo, YunSeok
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BR-scaling?

• Mass of the Hadron as a decreasing function of
  baryon density. (Brown-Rho)
• Motive of br-scalingMass comes from the chiral
  sym. breaking(cf. in ads, from confinement)As T
  or mu goes up, chiral symmetry is restored.
  Therefore m?0.

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Baryons in AdS/CFT

• Consider D5 enclosing D3 ? Chern-Simons coupling
  gives flux induced charge Nc.
• Need to cancel by attaching fundamental string

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Baryon Density

• Smear out the 1-baryon confifuration into uniform
  density along the 3 spatial direction.

• red string length need to be minimized ? 0
• Force balance need to be imposed

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Baryon chemical potential

• Suggested to be tail of BRANE-FIELD A_0by
  Kim-Sin-Zahed (hep-th/0608046)vector domination
  determines
• Horigome-Tanii (hep-th/0608198)Use eq. of Motion
  for A_0 without source

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Some issues in chemical pot. I

• Definition of chemical potentialNakamura, Seo,
  Sin, Yogendran (0611024)
• Karch et.al
• The difference gives a deep differencewhether
  there is a source in low temperature phase or
  not. (Is A(z)const. Physical in 5d?)

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System with conserved charge
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Some issues in chemical pot. II

• Can there be a Minkowski Embedding?
• Black hole embedding v.s Minkoswki brane

NSSY YES Classify all the possible solution and
interpret by string theory objects
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• Kobayashi et.al (hep-th/0611099)
• No ME in the presence of baryon charge.
• If we introduce only quarks Yes.
• But If we introduce the baryon source,
• we may have ME.

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Quark Phase (D3/D7)

• String is connecting D7 and horizon
  ??
• D7 brane deformation with spiky structure.

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Baryon Phase of D3/D7

• String is connecting D7 and baryon vertex
  ??
• D7 brane deformation without spiky structure.
• ME brane

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Back to the BR-scaling

• O. Bergman et.al SS-model with Baryon vertex
• In both Low and high temperature, the tip of the
  D8D8bar eventually goes higher.

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It means that the Baryon mass is going up as the
density goes up, contrary to BR-scaling.
What is going on? Local U(1) ? Only repulsive
forceNeed attraction!
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Q How to introduce attraction?

• Attraction! Attraction! make the Baryon mass
  decreases as function of density.
• 1. Consider non-abelian DBI and use Instanton
  baryon (Zahed,K.Kim,SJS compactify R4?S4, dilute
  instanton approximation/ Multi-instanton
  solution).
• 2. Consider Effective Fermionic theory of HRYY
  and use instanton solutions (NakamuraSJS)
• 3. Consider 10 embedding geometry of baryon
  vertex in other set up (Yunseok Seo, SJS )
  Todays topic.

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Setup D3/D7(21) or D4/D6(31)with confinment
and add Baryon
Idea Position of tip determines the mass of
D5 We can pull down by Gravity and force balance
condition Unlike SS, it is not possible to
decrease the total energy by Increasing the
height of the tip.
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D3/D7 with confinement (21) setup.
Start with black D3 solution and take double
wick rotation
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Embedding of D7 and induced metric
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Action and eqm for D7
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For Baryon vertex
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D5 has fixed charge! Need Ham.
Solve eq. of Motion !
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Muti-baryon? by smearing out

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Force balance condition
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D7 configuration for fixed quark mass

• Solve D7 configuration numerically
• incoorperating FBC
• ?Determine the Uc? Determine mass of D5 (
  Baryon mass)

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Mqgtm_c U0,
Mqltm_c,

• There is a critical current quark mass

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Conclusion

• BR scaling works for some model for large quark
  mass.
• Wait to compare the result of other aspect of
  the calculations are finished.
• To be continued!