QGP and Hadrons in Dense medium: a holographic view @ 2nd ATHIC 2008. 10.13 based on works with X....
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![Page 1: QGP and Hadrons in Dense medium: a holographic view @ 2nd ATHIC 2008. 10.13 based on works with X. Ge, Y. Matsuo, F. Shu, T. Tsukioka(APCTP), archiv:0806.4460.](https://reader030.fdocuments.us/reader030/viewer/2022032414/56649ef45503460f94c06bc6/html5/thumbnails/1.jpg)
QGP and Hadrons in Dense medium:
a holographic view
@ 2nd ATHIC 2008. 10.13
based on works withX. Ge, Y. Matsuo, F. Shu, T. Tsukioka(APCTP), archiv:0806.4460
J. Hur, K.Kim (KIAS), archiv:0809.4541S. Seo (HYU), JHEP 0804:010,2008
Sang-Jin Sin (Hanyang U.)
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Introduction
String theory began as a hadron theory
After 40 yearsstring theory is back to Str. Int. with the idea of gague/gravity duality.
Can we do something for QCD?
N=4 SYM has difference as much as similarity: SUSY, extra deg. of freedom
appeal to universality-> hydro.
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Universality and AdS/QCD
High temperature phase -> Broken SUSY -> Share more with QCD
a quantity in Hydrodynamics -> Low frequency and Long wave length
As far as dual gravity is valid->
perhaps, ads/qcd in medium is more relevant to qcd than in vacuum.
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Plan
Hydrodynamics I: Green function and Kubo formula [archiv:0806.4460]
Hydrodynamics II: Metallic QGP[archiv:0809.4541]
Baryons in finite chemical potential[JHEP 0804:010,2008]
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Hydrodynamics I: Transport coefficients
X. Ge, Y. Matsuo, F. Shu, T. Tsukioka(APCTP), archiv:0806.4460
Finite temperature (and density)<-> (charged) black hole
Linear Response theory: Transport coefficients <- Kubo formula<- zero frequency limit of G_R <- ads/cft boundary action.
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AdS R-N black hole
Solution to the eq. of M:
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Thermodynamics
temperature, entropy, energy
pressure, charge density and chemical pot.
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Perturbations around RN
perturbed Eintein eq.
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perturbed Maxwell eq.
Gauge choice and Fourier mode
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Classification of modes
O(2) classification.
We consider vector and scalar types
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Vector type pert.
def. new variables:
eq. of Motion
Remark: q=0-> A-h decouples
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Master equations
Similarly tensor type has simple eq.
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Diffusion pole
Infalling BC at horizon
perturbative solution near boundary
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On-shell action
Others are similar.
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Correlation functions
Diffusion constant:
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diffusion const.
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shear Viscosity
Kubo formula
Green functions for tensor pert.
Shear viscosity
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Transport coefficients.
Thermal conductivity
Consistency:
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viscosity
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Thermal conductivity
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Charged black hole & baryon density:
archiv:0707.2919, SJS
Consider a D-brane that fills the whole space. then the response of the metric to the charge is the same whether it is R-charge or baryon charge.
Unique minimal coupling between Maxwell & Einstein fields.
Therefore we can interpret the the charge of the RN black hole as the baryon charge density.
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Hydrodynamics II: archiv:0809.4521, Hur+Kim+SJS
Einstein eq. in the bulk <-> Fluid dynamics in the boundary.
This method yields:
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Consistency bet. I and II
From the Hydro I ( Kubo formula)
We can show that this is the same as
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Wiedermann-Franz law
This indicates the Metallic property of sQGP
Can we measure the conductivity of sQGP?
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Medium dependence of conductivities
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So far, QGP regimewhat about hadrons?
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Baryon mass in finite density: JHEP0804:010,2008, Seo +SJS
In general, interested in fininte density and temperature.
For QGP, black hole background and T is easy.string provide baryon charge.
In confining regime, temperature dependence is hard to encode due to large N nature of ads/cft.
set T=0 with non-zero density.
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Hologaphic view of baryon density
In 4d field theory: chemical potential is a constant gauge potential.
In holographic view: 5d electric potential, phi, is a created by the charge, which is the string end points.
choose the value at the horizon to be 0.
phi at boundary is the chemical pt.
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a Baryon is a compact brane connected to flavor branes by N_c strings : fig. a
strings are energy costly -> D branes deform to reduce the string length 0: fig. b
Force balancing condition gives connection condi
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Baryon mass in medium:It falls but not in small current quark mass
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Conclusion
Green functions and Transport coefficients calculated.
QGP may have a another surprising property: Metallic conductivity!
baryon mass falls in medium, perhaps.
Gravity dual of gauge theory may become a powerful tool for the heavy ion collision.