1. 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

2.  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

3. Perturbation theory Lattice Our understanding of gauge theories is limited…

4. Perturbation theory Lattice Conjecture: specific gauge theory in 4 dim = specific string theory in 10 dim Dual string theory

5. Perturbation theory 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

6. 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

7. 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 gravity 4-dim gauge theory – large N, strong coupling

8. Transport (kinetic) coefficients Shear viscosity Bulk viscosity Charge diffusion constant Thermal conductivity Electrical conductivity

9. 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

10. 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)

11. 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:

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

13. 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.

14. A viscosity bound conjecture P.Kovtun, D.Son, A.S., hep-th/0309213, hep-th/0405231

15. A hand-waving argument Gravity duals fix the coefficient: Thus

16. Shear viscosity at non-zero chemical potential Reissner-Nordstrom-AdS black hole with three R charges (Behrnd, Cvetic, Sabra, 1998) We still have J.Mas D.Son, A.S. O.Saremi K.Maeda, M.Natsuume, T.Okamura (see e.g. Yaffe, Yamada, hep-th/0602074)

17. Thermal conductivity Non-relativistic theory: Relativistic theory: Kubo formula: InSYM with non-zero chemical potential One can compare this with the Wiedemann-Franz law for the ratio of thermal to electric conductivity:

18. Analytic structure of the correlators Weak coupling: S. Hartnoll and P. Kumar, hep-th/0508092 Strong coupling: A.S., hep-th/0207133

19. Spectral function and quasiparticles A B C A: scalar channel B: scalar channel - thermal part C: sound channel

20. Photon and dilepton emission from supersymmetric Yang-Mills plasma S. Caron-Huot, P. Kovtun, G. Moore, A.S., L.G. Yaffe, in preparation

21. Photons interacting with matter: Photon emission from SYM plasma To leading order in Mimicby gauging global R-symmetry Need only to compute correlators of the R-currents

22. Photoproduction rate in SYM (Normalized) photon production rate in SYM for various values of ‘t Hooft coupling

23. How far is SYM from QCD? pQCD (dotted line) vs pSYM (solid line) at equal coupling (and =3) pQCD (dotted line) vs pSYM (solid line) at equal fermion thermal mass (and =3)

24. 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?

25. 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