Dual gravity approach to near-equilibrium processes
in strongly coupled gauge theories
Andrei Starinets
Hadrons and Strings Trento
July 20, 2006
Perimeter Institute for Theoretical Physics
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
Perturbationtheory
Lattice
Our understanding of gauge theories is limited…
Perturbationtheory
Lattice
Conjecture: specific gauge theory in 4 dim =specific string theory in 10 dim
Dual
string th
eory
Perturbationtheory
Lattice
Dual gravity
In practice: gravity (low energy limit of string theory) in 10 dim =4-dim gauge theory in a region of a parameter space
Can add fundamental fermions with
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
M,J,Q
Holographically dual system in thermal equilibrium
M, J, Q
T S
Gravitational fluctuations Deviations from equilibrium
????
and B.C.
Quasinormal spectrum
10-dim gravity4-dim gauge theory – large N,
strong coupling
Transport (kinetic) coefficients
• Shear viscosity
• Bulk viscosity
• Charge diffusion constant
• Thermal conductivity
• Electrical conductivity
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-dimgravity background involving AdS-Schwarzschild black hole
Computing transport coefficients from “first principles”
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
Fluctuation-dissipation theory(Callen, Welton, Green, Kubo)
What is known?
• in the limit • universal for a large class of theories
Bulk viscosity for non-conformal theories
Shear viscosity/entropy ratio:
• in the limit • model-dependent
R-charge diffusion constant for N=4 SYM:
Shear viscosity in SYM
Correction to : A.Buchel, J.Liu, A.S., hep-th/0406264
(perturbative thermal gauge theory)
Universality of
Theorem:
For any thermal gauge theory (with zero chemicalpotential), the ratio of shear viscosity to entropy density is equal to in the regime describedby a corresponding dual gravity theory
Remark:
Gravity dual to QCD (if it exists at all) is currentlyunknown.
A viscosity bound conjecture
P.Kovtun, D.Son, A.S., hep-th/0309213, hep-th/0405231
A hand-waving argument
Gravity duals fix the coefficient:
Thus
Shear viscosity at non-zero chemical potential
Reissner-Nordstrom-AdS black hole
with three R charges
(Behrnd, Cvetic, Sabra, 1998)
We still have
J.MasD.Son, A.S.O.SaremiK.Maeda, M.Natsuume, T.Okamura
(see e.g. Yaffe, Yamada, hep-th/0602074)
Thermal conductivityNon-relativistic theory:
Relativistic theory:
Kubo formula:
In SYM with non-zero chemical potential
One can compare this with the Wiedemann-Franz lawfor the ratio of thermal to electric conductivity:
Analytic structure of the correlators
Weak coupling: S. Hartnoll and P. Kumar, hep-th/0508092
Strong coupling: A.S., hep-th/0207133
Spectral function and quasiparticles
A
B
CA: scalar channel
B: scalar channel - thermal part
C: sound channel
Photon and dilepton emission from supersymmetric Yang-Mills plasma
S. Caron-Huot, P. Kovtun, G. Moore, A.S., L.G. Yaffe, in preparation
Photons interacting with matter:
Photon emission from SYM plasma
To leading order in
Mimic by gauging global R-symmetry
Need only to compute correlators of the R-currents
Photoproduction rate in SYM
(Normalized) photon production rate in SYM for various values of ‘t Hooft coupling
How far is SYM from QCD?
pQCD (dotted line) vspSYM (solid line)at equal coupling
(and =3)
pQCD (dotted line) vspSYM (solid line)
at equal fermion thermal mass(and =3)
Outlook
How universal is ? How useful are the N=4 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 (other talks at this workshop)? Understanding corrections?
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
The result for the shear viscosity turns out to be universal for all such theories in the limit if infinitely strong coupling
At the moment, this method is the only theoretical tool available to study the near-equilibrium regime of strongly coupled thermal field theories
Prospects for experimental verification are not hopeless