# Presentation: 223367

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

- Andrei Starinets

***                  ******SEWM-2006***
***Brookhaven National Laboratory ***

- May 10, 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

## Perturbation

- theory

- Lattice

- Our understanding of gauge theories is limited...

## Dual

- Perturbation
- theory

- Lattice

- Conjecture:
- specific gauge theory in 4 dim =
- specific string theory in 10 dim

-   string   theory

## 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

## 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

## 10-dim gravity

**Holographically dual system**
**     ****in thermal equilibrium**

**M, J, Q **

- T       S

- Gravitational fluctuations

- Deviations from equilibrium

- ????

- and B.C.

- Quasinormal spectrum

- 4-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-dim
- gravity 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 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.

## 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.Mas
- D.Son, A.S.
- O.Saremi
- K.Maeda, M.Natsuume, T.Okamura

- (see e.g. Yaffe, Yamada, hep-th/0602074)

## 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:

## 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**

**C**

**A: scalar channel**

**B: scalar channel - thermal part**

**C: sound channel**

##    Photon and dilepton emission

-    Photon and dilepton emission
- from strongly coupled YM plasma

## Photoproduction rate

-         Perturbative QCD
-  (Arnold, Moore, Yaffe, 2001)

- N=4 SYM ++

- (see talk by P.Kovtun)

## 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?
-  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