Dual gravity approach to near-equilibrium processes in strongly coupled gauge theories

1. Dual gravity approach to near-equilibrium processes in strongly coupled gauge theories Andrei Starinets Perimeter Institute for Theoretical Physics Hadrons and Strings Trento July 20, 2006

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

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

5. 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

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. 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

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

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” 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

11. 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 N=4 SYM:

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

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 Thus Gravity duals fix the coefficient:

16. 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

17. 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:

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

19. Spectral function and quasiparticles A B A: scalar channel C 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. Photon emission from SYM plasma Photons interacting with matter: To leading order in Mimic by 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 • 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