Dual gravity approach to nearequilibrium processes in strongly coupled gauge theories

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Dual gravity approach to near-equilibrium
processes in strongly coupled gauge theories
Andrei Starinets
Perimeter Institute for Theoretical Physics
SEWM-2006 Brookhaven National
Laboratory
May 10, 2006
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• Non-equilibrium regime of thermal gauge theories
  is of
• interest for RHIC and early universe physics

• This regime can be studied in perturbation
  theory, assuming
• the system is a weakly interacting one.
  However, this is often
• NOT the case. Nonperturbative approaches
  are needed.

• Lattice simulations cannot be used directly for
  real-time
• processes.

• Gauge theory/gravity duality CONJECTURE provides
  a
• theoretical tool to probe non-equilibrium,
  non-perturbative
• regime of SOME thermal gauge theories

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Our understanding of gauge theories is limited
Perturbation theory
Lattice
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Conjecture specific gauge theory in 4 dim
specific string theory in 10 dim
Perturbation theory
Dual
string theory
Lattice
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In practice gravity (low energy limit of string
theory) in 10 dim 4-dim gauge theory in a
region of a parameter space
Perturbation theory
Dual gravity
Lattice
Can add fundamental fermions with
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Hydrodynamic properties of strongly interacting
hot plasmas in 4 dimensions
can be related (for certain models!)
to fluctuations and dynamics of 5-dimensional
black holes
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4-dim gauge theory large N, strong coupling
10-dim gravity
M,J,Q
Holographically dual system in thermal
equilibrium
M, J, Q
T S
Deviations from equilibrium
Gravitational fluctuations
????
and B.C.
Quasinormal spectrum
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Transport (kinetic) coefficients

• Shear viscosity
• Bulk viscosity
• Charge diffusion constant
• Thermal conductivity
• Electrical conductivity

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Gauge/gravity dictionary determines correlators
of gauge-invariant operators from gravity (in the
regime where gravity description is valid!)
For example, one can compute the correlators such
as
by solving the equations describing fluctuations
of the 10-dim gravity background involving
AdS-Schwarzschild black hole
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Computing transport coefficients from first
principles
Fluctuation-dissipation theory (Callen, Welton,
Green, Kubo)
Kubo formulae allows one to calculate transport
coefficients from microscopic models
In the regime described by a gravity dual the
correlator can be computed using the gauge
theory/gravity duality
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What is known?

• Shear viscosity/entropy ratio

• in the limit
• universal for a large class of theories

• Bulk viscosity for non-conformal theories

• in the limit
• model-dependent

• R-charge diffusion constant for N4 SYM

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Shear viscosity in SYM
(perturbative thermal gauge theory)
Correction to A.Buchel, J.Liu,
A.S., hep-th/0406264
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Universality of

Theorem
For any thermal gauge theory (with zero
chemical potential), the ratio of shear
viscosity to entropy density is equal to
in the regime described by a corresponding
dual gravity theory
Remark
Gravity dual to QCD (if it exists at all) is
currently unknown.
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A viscosity bound conjecture
P.Kovtun, D.Son, A.S., hep-th/0309213,
hep-th/0405231
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A hand-waving argument
Thus
Gravity duals fix the coefficient
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Shear viscosity at non-zero chemical potential
Reissner-Nordstrom-AdS black hole with three R
charges (Behrnd, Cvetic, Sabra, 1998)
(see e.g. Yaffe, Yamada, hep-th/0602074)
J.Mas D.Son, A.S. O.Saremi K.Maeda, M.Natsuume,
T.Okamura
We still have
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Thermal conductivity
Non-relativistic theory
Relativistic theory
Kubo formula
In
SYM with non-zero chemical potential
One can compare this with the Wiedemann-Franz
law for the ratio of thermal to electric
conductivity
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Analytic structure of the correlators
Strong coupling A.S., hep-th/0207133
Weak coupling S. Hartnoll and P. Kumar,
hep-th/0508092
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Spectral function and quasiparticles
A
B
A scalar channel
C
B scalar channel - thermal part
C sound channel
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Photon and dilepton emission from strongly
coupled YM plasma
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Photoproduction rate
(see talk by P.Kovtun)
Perturbative QCD (Arnold, Moore, Yaffe,
2001)
N4 SYM
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Outlook

• How universal is ?
• How useful are the N4 spectral functions
• for thermal QCD lattice simulations?
  
• Can we get a meaningful comparison of
• photon and lepton production rates
• obtained using pQCD, lattice, gauge/gravity
  duality,
• RHIC?
• Gravity duals of theories with fundamental
  fermions
• phase transitions, meson spectrum,
• transport properties, flavor currents?
• Understanding corrections?

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Epilogue

• On the level of theoretical models, there exists
  a connection
• between near-equilibrium regime of certain
  strongly coupled
• thermal field theories and fluctuations of
  black holes

• This connection allows us to compute transport
  coefficients
• for these theories

• At the moment, this method is the only
  theoretical tool
• available to study the near-equilibrium
  regime of strongly
• coupled thermal field theories

• The result for the shear viscosity turns out to
  be universal
• for all such theories in the limit if
  infinitely strong coupling

• Prospects for experimental verification are not
  hopeless