qm06 Liu

String theory and heavy ion collisions : 

String theory and heavy ion collisions Hong Liu HL, Krishna Rajagopal, Urs A. Wiedemann hep-ph/0605178, PRL in press hep-ph/0607062, submitted to PRL and to appear Massachusetts Institute of Technology

String theory and heavy ion collisions: 

String theory and heavy ion collisions Here, I would like to convince you this is likely to be the first chapter of a long story. In later chapters, many more experimental results could be explained, and predictions can be made. The AdS/CFT computation of the shear viscosity: could ``explain’’ the perfect fluid observed at RHIC possibly a universal lower bound Son and Kapusta’s talks

Slide3: 

Chapter n: AdS/CFT and Jet quenching

Parton energy loss in QGP: 

Parton energy loss in QGP

Slide5: 

Wanted: a first principle computation of : 5-15 GeV2/fm

Slide6: 

The main theoretical techniques for dealing with strongly coupled problems are lattice calculations. Lattice techniques are not well adapted to calculate transport coefficients, or dynamical processes of any sort. New theoretical techniques needed!

AdS/CFT correspondence: 

AdS/CFT correspondence Classical gravity limit N = 4 Super-Yang-Mills theory in 4d with SU(NC) Maldacena (1997), Gubser, Klebanov,Polyakov; Witten (1998) Apply to both dynamical and thermodynamic observables. YM observables at infinite NC and infinite coupling can be computed using classical gravity A string theory in 5d AdS Finite temperature Large NC and strong coupling limit Black hole in AdS5

Slide8: 

Need a non-perturbative definition of Compute in strongly coupled Super-Yang-Mills theory using AdS/CFT Strategy Similar strategy was used to compute the shear viscosity.

Slide9: 

Caution: N = 4 Super-Yang-Mills theory is NOT QCD Later: Using sQGP of N = 4 SYM to understand sQGP of RHIC may NOT be far-fetched. Now: Accumulate data points

: a non-perturbative formulation: 

: a non-perturbative formulation : multiple rescatterings of hard particles with the medium Hard: weakly coupled Soft: likely strongly coupled

Soft scatterings : 

Soft scatterings Amplitude for a particle propagating in the medium Soft scatterings are captured by Light like Wilson lines. Zakharov (1997); Wiedemann (2000)

A non-perturbative definition of : 

A non-perturbative definition of Wiedemann (2000)

Wilson loop from AdS/CFT: 

Wilson loop from AdS/CFT Black hole in AdS spacetime: radial coordinate r, horizon: r=r0 constant r surface: (3+1)-dim Minkowski spacetime horizon Recipe: Maldacena (1998); Rey and Yee (1998) : area of string worldsheet with boundary C

Finding S(C) : 

Finding S(C) Not more difficult than finding the Catenary ! Wilson loop can be considered as the spacetime trajectories of a quark and antiquark pair. Key: open string connecting the quark pair can venture into the radial dimension. Finding S (C) : finding the shape of the string hanging from the spatial infinity of a black hole.

Shape of the string : 

Shape of the string The string hangs down from infinity and touches the horizon. Interactions between the quark and the medium Interaction of the string with the horizon of a black hole.

of N=4 SYM theory: 

of N=4 SYM theory It is not proportional to number of scattering centers Experimental estimates: 5-15 GeV2/fm BDMPS transport coefficient reads:

Jet quenching in a wind: 

Jet quenching in a wind

Summary: 

Summary In QGP of QCD, the energy loss of a high energy parton can be described perturbatively up to a non-perturbative jet-quenching parameter. We calculate the parameter in N=4 SYM (not necessarily full energy loss of SYM) It appears to be close to the experimental value. Is the agreement meaningful?

Is agreement meaningful?: 

Is agreement meaningful? Conformal no asymptotic freedom, no confinement supersymmetric no chiral condensate no dynamical quarks, 6 scalar and 4 Weyl fermionic fields in the adjoint representation. Physics near vacuum and at very high energy is very different from that of QCD N=4 SYM theory

Is agreement meaningful? (continued): 

conformal no asymptotic freedom, no confinement supersymmetric (badly broken ) no chiral condensate no dynamical quarks, 6 scalars and 4 fermions in the adjoint representation. N=4 SYM at finite T QCD at T ~TC -3 TC Is agreement meaningful? (continued) near conformal (lattice) not intrinsic properties of sQGP not present not present may be taken care of by proper normalization

Maybe the agreement is not an accident after all !: 

Maybe the agreement is not an accident after all ! Experimental estimates: 5-15 GeV2/fm Take: Caveat: AdS/CFT calculation is in the infinite NC and infinite coupling limit

for other theories: 

for other theories General conformal field theories (CFT) with a gravity dual: (large N and strong coupling) aCFT : central charge Theories near conformal: corrections small Finite coupling and NC corrections: hard R-charge chemical potentials: Buchel Lin, Matsuo, Avramis, Sfetsos, Armesto,Edelstein, Mas, ……. Armesto, Edelstein and Mas corrections mall when chemical potential is small

Drag force for heavy quarks in N=4 SYM: 

Drag force for heavy quarks in N=4 SYM Herzog, Karch, Kovtun, Kozcaz, Yaffe; Gubser, ……. Fluctuation-dissipation theorem assumes the quark is in equilibrium with the medium: does not apply to high energy jet

Slide24: 

Chapter n+1: Quarkonium suppression: predictions for LHC or RHIC II

Quarkonium suppression at high PT: 

Quarkonium suppression at high PT Techniques discussed above can also be used to calculate screening length between a quark pair. Static quarks: great success from lattice calculation Heavy quarks produced in heavy ion collisions typically move relative to the medium: hard to do using lattice. HL,Rajagopal,Wiedemann

Conclusions: a nice honeymoon: 

Conclusions: a nice honeymoon AdS/CFT provides powerful tools to understand dynamics of strong coupled gauge theories. Expect many more chapters to be written for the marriage between string theory and physics of QCD in extreme conditions.