RHIC physics and AdS/CFT Amos Yarom, Munich TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A A A A A A A together with: S. Gubser and S. Pufu

Overview The quark gluon plasma Energy g YM 1 ~170 MeV ?

Overview The quark gluon plasma N=4 SYM plasma via AdS/CFT AdS/CFT J. Maldacena

Overview The quark gluon plasma N=4 SYM plasma via AdS/CFT ?

Overview The quark gluon plasma N=4 SYM plasma via AdS/CFT Energy loss of a moving quark

Overview The quark gluon plasma N=4 SYM plasma via AdS/CFT Energy loss of a moving quark

Overview The quark gluon plasma N=4 SYM plasma via AdS/CFT Energy loss of a moving quark Summary

The quark gluon plasma at RHIC RELATIVISTICRELATIVISTIC HEAVYHEAVY IONION COLLIDERCOLLIDER

Jet quenching 197 × pTpT

Jet quenching (Phenix, 2005)

Friction coefficient for QCD plasma

N=4 SYM plasma via AdS/CFT AdS/CFT J. Maldacena AdS 5 CFT Empty AdS 5 Vacuum L4/’2L4/’2 g YM 2 N  L 3 /2 G 5 N2N2 J. Maldacena hep-th/

T>0 N=4 SYM plasma via AdS/CFT AdS 5 CFT AdS 5 BH Thermal state L4/’2L4/’2 g YM 2 N  L 3 /2 G 5 N2N2 E. Witten hep-th/ Horizon radiusTemperature Empty AdS 5 Vacuum J. Maldacena hep-th/

AdS Black holes z0z0 z 0 x1x1 x i, t AdS 5 CFT AdS 5 BH Thermal state L4/’2L4/’2 g YM 2 N  L 3 /2 G 5 N2N2 E. Witten hep-th/ Horizon radiusTemperature z0z0 1/  T

AdS/CFT J. Maldacena Friction coefficient AdS 5 CFT J. Maldacena hep-th/ Massive parton Endpoints of an open string z0z0 z 0 ? (Gubser 2006, Holzhey, Karch, Kovtun, Kozcaz, Yaffe, 2006, Teaney Cassalderrey-Solana, 2006)

Friction coefficient AdS 5 CFT J. Maldacena hep-th/ Massive parton Endpoints of an open string z0z0 z 0 ? (Gubser 2006, Holzhey, Karch, Kovtun, Kozcaz, Yaffe, 2006, Teaney Cassalderrey-Solana, 2006)

Friction coefficient z0z0 z 0 F F (Gubser 2006, Holzhey, Karch, Kovtun, Kozcaz, Yaffe, 2006, Teaney Cassalderrey-Solana, 2006)

Friction coefficient AdS/CFT J. Maldacena (Gubser 2006, Holzhey, Karch, Kovtun, Kozcaz, Yaffe, 2006, Teaney Cassalderrey-Solana, 2006)

Measurables which have been compared Friction coefficient Energy density Shear viscosity Jet quenching parameter (Policastro, Son, Starinets, 2001) (Liu, Rajagopal, Wiedemann, 2006) (Gubser 2006, Holzhey, Karch, Kovtun, Kozcaz, Yaffe, 2006, Teaney Cassalderrey-Solana, 2006) (Gubser, Klebanov, Peet, 1996)

Measuring jets



Measuring di-jets 

Measuring di-jets (STAR, )

Measuring di-jets (STAR, )  = 

Measuring di-jets (STAR, )  » 

Creation of sound waves (Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)

Creation of sound waves (Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)

Mach cones and di-jets (Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)  » 

Mach cones in N=4 SYM AdS 5 CFT z0z0 z 0

The energy momentum tensor AdS 5 CFT AdS black hole Metric fluctuations z0z0 z 0 G mn  z,k)

The energy momentum tensor z0z0 z 0

Gauge choice Cylindrical symmetry Tensor modes Vector modes

The energy momentum tensor Tensor modes Vector modes + first order constraint

The energy momentum tensor Tensor modes Vector modes + first order constraint Scalar modes + 3 first order constraints

Energy density for v=3/4 Over energy Under energy

v=0.75 v=0.58 v=0.25

Small momentum approximations 1-3v 2 > 0 (subsonic)

Small momentum approximations 1-3v 2 > 0 (subsonic) Re(K 1 ) Im(K 1 ) v decreases v increases X 1 > 0 X 1 < 0

Small momentum approximations 1-3v 2 < 0 (supersonic) Re(K 1 ) Im(K 1 ) 1-3v 2 = 0 v increases ? ? X 1 > 0 X 1 < 0 X1X1

Small momentum approximations 1-3v 2 < 0 (supersonic) 1-3v 2 > 0 (subsonic)

Small momentum approximations

Re(K 1 ) Im(K 1 ) c s 2 =1/3  s =1/3

Multi-scale analysis Large distances – linear hydrodynamic picture valid Intermediate distances – nonlinear hydrodynamics Short momenta – Strong dissipative effects

Energy density for v=3/4

0

v=0.75 v=0.58 v=0.25

Large momentum approximations

Wakes

Mach cones, wakes and di-jets (Casalderrey-Solana, Shuryak, Teaney, 2004, 2006)

Mach cones, wakes and di-jets (Casalderrey-Solana, Shuryak, Teaney, 2004, 2006) (STAR, )

The Poynting vector z0z0 z 0

V=0.25 S1S1 S?S? V=0.58 V=0.75 (Gubser, Pufu, AY, 2007)

Re(K 1 ) Im(K 1 ) Small momentum asymptotics Sound Waves ? (Gubser, Pufu, AY, 2007) X1X1

Small momentum asymptotics (Gubser, Pufu, AY, 2007)

The poynting vector V=0.25 S1S1 S?S? V=0.58 V=0.75 (Gubser, Pufu, AY, 2007)

Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, 2006 Gubser, Pufu, AY, 2007)

Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, 2006 Gubser, Pufu, AY, 2007) z0z0 z 0 FF ? Just been calculated

Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, 2006, Gubser, Pufu, AY, 2007)

Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, 2006, Gubser, Pufu, AY, 2007) =

Universality (Gubser, AY,2007) z0z0 z 0

Universality (Gubser, AY, 2007) z0z0 0 z

Summary N=4 SYM plasma exhibits a Mach cone and a wake at large distances, where the hydrodynamic approximation is valid. The laminar wake behind the quark is a universal feature of theories with string duals, and the ratio of energy carried by the wake to the drag force is 1:v 2. This wake is difficult to reconcile with current experimental data.