Gauge/gravity duality and transport in hot and dense nuclear matter Andrei Starinets Rudolf Peierls Centre for Theoretical Physics Oxford University Oxford Elementary Particle Physics Seminars 11 November 2008

Heavy ion collision experiments at RHIC (2000-current) and LHC (2009-??) create hot and dense nuclear matter known as the quark-gluon plasma (note: qualitative difference between p-p and Au-Au collisions) Evolution of the plasma fireball is described by relativistic fluid dynamics (relativistic Navier-Stokes equations) Need to know thermodynamics (equation of state) kinetics (first- and second-order transport coefficients) in the regime of intermediate coupling strength: initial conditions (initial energy density profile) thermalization time (start of hydro evolution)

freeze-out conditions (end of hydro evolution) relativistic hydrodynamics heavy-ion physics technicolor thermal QCD AdS/CFT

AdS/QCD quantum gravity quantum liquids black hole physics non-relativistic AdS/CFT condensed matter physics Quantum field theories at finite temperature/density

Equilibrium Near-equilibrium entropy equation of state . transport coefficients emission rates

perturbative non-perturbative Lattice pQCD perturbative non-perturbative ???? kinetic theory 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 Energy density vs temperature for various gauge theories

Ideal gas of quarks and gluons Ideal gas of hadrons Figure: an artistic impression from Myers and Vazquez, 0804.2423 [hep-th] The challenge of RHIC (continued) Rapid thermalization

?? Large elliptic flow Jet quenching Photon/dilepton emission rates First-order transport (kinetic) coefficients Shear viscosity Bulk viscosity Charge diffusion constant

Supercharge diffusion constant Thermal conductivity Electrical conductivity * Expect Einstein relations such as to hold Hydrodynamics: fundamental d.o.f. = densities of conserved charges Need to add constitutive relations!

Example: charge diffusion Conservation law Constitutive relation [Ficks law (1855)] Diffusion equation Dispersion relation Expansion parameters: 10-dim gravity

M,J,Q 4-dim gauge theory large N, strong coupling Holographically dual system in thermal equilibrium M, J, Q T Gravitational fluctuations

S Deviations from equilibrium ???? and B.C. Quasinormal spectrum From brane dynamics to AdS/CFT correspondence Open strings picture:

dynamics of coincident D3 branes at low energy is described by Closed strings picture: dynamics of coincident D3 branes at low energy is described by conjectured exact equivalence

Maldacena (1997); Gubser, Klebanov, Polyakov (1998); Witten (1998) AdS/CFT correspondence conjectured exact equivalence Generating functional for correlation functions of gauge-invariant operators

Latest test: Janik08 String partition function In particular Classical gravity action serves as a generating functional for the gauge theory correlators The bulk and the boundary in AdS/CFT correspondence UV/IR: the AdS metric is invariant under

z plays a role of inverse energy scale in 4D theory z 5D bulk (+5 internal dimensions) 0 4D boundary supersymmetric Yang-Mills

is the harmonic oscillator of the XXI century! supersymmetric YM theory Gliozzi,Scherk,Olive77 Brink,Schwarz,Scherk77 Field content: Action:

(super)conformal field theory = coupling doesnt run AdS/CFT correspondence is the simplest example of the gauge/string

(gauge/gravity) duality 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 Computing transport coefficients from dual gravity Assuming validity of the gauge/gravity duality, all transport coefficients are completely determined by the lowest frequencies in quasinormal spectra of the dual gravitational background (D.Son, A.S., hep-th/0205051, P.Kovtun, A.S., hep-th/0506184) This determines kinetics in the regime of a thermal theory

where the dual gravity description is applicable Transport coefficients and quasiparticle spectra can also be obtained from thermal spectral functions First-order transport coefficients in N = 4 SYM in the limit Shear viscosity Bulk viscosity for non-conformal theories see Buchel et al; G.D.Moore et al

Gubser et al. Charge diffusion constant Supercharge diffusion constant Thermal conductivity Electrical conductivity (G.Policastro, 2008) Shear viscosity in

SYM perturbative thermal gauge theory S.Huot,S.Jeon,G.Moore, hep-ph/0608062 Correction to : Buchel, Liu, A.S., hep-th/0406264

Buchel, 0805.2683 [hep-th]; Myers, Paulos, Sinha, 0806.2156 [hep-th] Electrical conductivity in SYM Weak coupling: Strong coupling: * Charge susceptibility can be computed independently:

D.T.Son, A.S., hep-th/0601157 Einstein relation holds: Spectral function and quasiparticles A B C A: scalar channel

B: scalar channel - thermal part C: sound channel 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

Remarks: Extended to non-zero chemical potential: Benincasa, Buchel, Naryshkin, hep-th/0610145 Extended to models with fundamental fermions in the limit Mateos, Myers, Thomson, hep-th/0610184 String/Gravity dual to QCD is currently unknown A viscosity bound conjecture

P.Kovtun, D.Son, A.S., hep-th/0309213, hep-th/0405231 Viscosity measurements at RHIC Viscosity is ONE of the parameters used in the hydro models describing the azimuthal anisotropy of particle distribution -elliptic flow for particle species i Elliptic flow reproduced for e.g. Baier, Romatschke, nucl-th/0610108

Perturbative QCD: Chernai, Kapusta, McLerran, nucl-th/0604032 SYM: Elliptic flow with color glass condensate initial conditions Luzum and Romatschke, 0804.4015 [nuc-th] Elliptic flow with Glauber initial conditions

Luzum and Romatschke, 0804.4015 [nuc-th] Viscosity/entropy ratio in QCD: current status Theories with gravity duals in the regime where the dual gravity description is valid Kovtun, Son & A.S; Buchel; Buchel & Liu, A.S QCD: RHIC elliptic flow analysis suggests QCD: (Indirect) LQCD simulations H.Meyer, 0805.4567 [hep-th]

Trapped strongly correlated cold alkali atoms T.Schafer, 0808.0734 [nucl-th] Liquid Helium-3 (universal limit) Shear viscosity at non-zero chemical potential Reissner-Nordstrom-AdS black hole with three R charges

(see e.g. Yaffe, Yamada, hep-th/0602074) We still have (Behrnd, Cvetic, Sabra, 1998) J.Mas D.Son, A.S. O.Saremi K.Maeda, M.Natsuume, T.Okamura Photon and dilepton emission

from supersymmetric Yang-Mills plasma S. Caron-Huot, P. Kovtun, G. Moore, A.S., L.G. Yaffe, hep-th/0607237 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 Photoproduction rate in SYM (Normalized) photon production rate in SYM for various values of t Hooft coupling Outlook Gravity dual description of thermalization ? Gravity duals of theories with fundamental fermions: - phase transitions - heavy quark bound states in plasma

- transport properties Finite t Hooft coupling corrections to photon emission spectrum Understanding 1/N corrections Phonino 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 of infinitely strong coupling Influences other fields (heavy ion physics, condmat) Three roads to universality of The absorption argument D. Son, P. Kovtun, A.S., hep-th/0405231

Direct computation of the correlator in Kubo formula from AdS/CFT A.Buchel, hep-th/0408095 Membrane paradigm general formula for diffusion coefficient + interpretation as lowest quasinormal frequency = pole of the shear mode correlator + Buchel-Liu theorem P. Kovtun, D.Son, A.S., hep-th/0309213, A.S., to appear, P.Kovtun, A.S., hep-th/0506184, A.Buchel, J.Liu, hep-th/0311175

Universality of shear viscosity in the regime described by gravity duals Gravitons component obeys equation for a minimally coupled massless scalar. But then . we get Since the entropy (density) is Analytic structure of the correlators

Strong coupling: A.S., hep-th/0207133 Weak coupling: S. Hartnoll and P. Kumar, hep-th/0508092 Pressure in perturbative QCD A hand-waving argument Thus Gravity duals fix the coefficient:

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: Effect of viscosity on elliptic flow