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

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