Jets in N=4 SYM from AdS/CFT Yoshitaka Hatta U. Tsukuba Y.H., E. Iancu, A. Mueller, arXiv: [hep-th] (JHEP) Y.H., T. Matsuo, arXiv: [hep-th]

Contents Introduction e^+e^- annihilation and Jets in QCD Jet structure at strong coupling Jet evolution at finite temperature

Strongly interacting matter at RHIC Observed jet quenching of high-pt hadrons is stronger than pQCD predictions.

Strongly interacting matter at RHIC Ideal hydro simulation works, suggesting short mean free path. low viscosity, strong jet quenching

The Regge limit of QCD Hadron-hadron total cross section grows with energy (‘soft Pomeron’) c.f., pQCD prediction (BFKL, ‘hard Pomeron’) or ?

 There are many phenomena at collider experiment which defy weak coupling approaches.  Study N=4 SYM as a toy model of QCD. (Interesting in its own right…) One can solve strong coupling problems using AdS/CFT. Think how it may (or may not?) be related to QCD later…  Possible applications to jet quenching at RHIC, or in the `unparticle’ sector at the LHC?  Lots of works on DIS. e^+e^- annihilation is a cross channel of DIS. Motivation Why N=4 SYM? Why study jets ? Strassler, arXiv: [hep-ph]

Deep inelastic scattering in QCD Two independent kinematic variables  Photon virtuality  Bjorken- Momentum fraction of a parton : Parton distribution function Count how many partons are there inside a proton. DGLAP equation

DIS vs. e^+e^- annihilation Bjorken variable Feynman variable Parton distribution function Fragmentation function crossing

Jets in QCD Average angular distribution reflecting fermionic degrees of freedom (quarks) Observation of jets in `75 provides one of the most striking confirmations of QCD

Fragmentation function Count how many hadrons are there inside a quark. Feynman-x First moment average multiplicity energy conservation Second moment

Evolution equation The fragmentation functions satisfy a DGLAP-type equation Take a Mellin transform Timelike anomalous dimension (assume )

Anomalous dimension in QCD Lowest order perturbation Soft singularity ~ Resummation Angle-ordering Mueller, `81

Inclusive spectrum largel-x small-x roughly an inverse Gaussian peaked at

N=4 Super Yang-Mills SU(Nc) local gauge symmetry Conformal symmetry SO(4,2) The ‘ t Hooft coupling doesn ’ t run. Global SU(4) R-symmetry  choose a U(1) subgroup and gauge it.

Type IIB superstring Consistent superstring theory in D=10 Supergravity sector admits the black 3- brane solution which is asymptotically Our universe AdS `radius’ coordinate

(anomalous) dimension mass `t Hooft parameter curvature radius number of colors string coupling constant The correspondence Take the limits and N=4 SYM at strong coupling is dual to weak coupling type IIB on Spectrums of the two theories match Maldacena, `97 CFT string

Dilaton localized at small DIS at strong coupling R-charge current excites metric fluctuations in the bulk, which then scatters off a dilaton (`glueball’) Cut off the space at (mimic confinement) Polchinski, Strassler, `02 Y.H. Iancu, Mueller, `07 We are here Photon localized at large

e^+e^- annihilation at strong coupling Hofman, Maldacena Y.H., Iancu, Mueller, Y.H. Matsuo arXiv: [hep-th] arXiv: [hep-th] arXiv: [hep-th] 5D Maxwell equation Dual to the 4D R-current

A reciprocity relation DGRAP equation Dokshitzer, Marchesini, Salam, ‘06 The two anomalous dimensions derive from a single function Basso, Korchemsky, ‘07 Application to AdS/CFT Assume this is valid at strong coupling and see where it leads to. Confirmed up to three loops (!) in QCD Mitov, Moch, Vogt, `06

Anomalous dimension in N=4 SYM Gubser, Klebanov, Polyakov, `02 Kotikov, Lipatov, Onishchenko, Velizhanin `05 Brower, Polchinski, Strassler, Tan, `06 Leading Regge trajectory Twist—two operators lowest mass state for given j lowest dimension operator for given j The `cusp’ anomalous dimension

Average multiplicity c.f. in perturbation theory, crossing c.f. heuristic argument Y.H., Iancu, Mueller ‘08 Y.H., Matsuo ‘08

Jets at strong coupling? The inclusive distribution is peaked at the kinematic lower limit 1 Rapidly decaying function for in the supergravity limit At strong coupling, branching is so fast and efficient. There are no partons at large-x !

Energy correlation function Hofman, Maldacena `08 Energy distribution is spherical for any Correlations disappear as All the particles have the minimal four momentum~ and are spherically emitted. There are no jets at strong coupling ! weak coupling strong coupling

Evolution of jets in a N=4 plasma Y.H., Iancu, Mueller `08 Solve the Maxwell equation in the background of Schwarzschild AdS_5 To compute correlation functions : Event horizon

Time-dependent Schrödinger equation 2 Solutions available only piecewise. Qualitative difference between t=0 horizon Minkowski boundary ‘low energy’ and ‘high energy’ : plasma saturation momentum To study time-evolution, add a weak t-dependence and keep only the 1 st t-derivative

low-energy, Early time diffusion solution with This represents diffusion up to time

Gauge theory interpretation IR/UV correspondence c.f., general argument from pQCD Farrar, Liu, Strikman, Frankfurt ‘88 is the formation time of a parton pair (a.k.a., the coherence time in the spacelike case)

low-energy Intermediate free streaming region solution with constant (group-) velocity motion

Gauge theory interpretation IR/UV correspondence is the transverse velocity Linear expansion of the pair

low-energy Falling down the potential solution with A classical particle with mass falling down the potential

Gauge theory interpretation disappear into the plasma start to `feel’ the plasma In-medium acceleration

The high energy case A new characteristic time No difference between the timelike/spacelike cases

The scale is the meson screening length Energy loss, meson screening length, and all that Liu, Rajagopal, Wiedemann, `06 WKP solution after the breakup features the trailing string solution Herzog, et al, ‘06, Gubser, ‘06 breakup

Energy loss, meson screening length, and all that Rate of enery flow towards the horizon Identical to the motion of our wavepacket Time to reach the horizon c.f., damping time of a gluon Gubser, Gulotta, Pufu, Rocha, [hep-th]

Branching picture at strong coupling Energy and virtuality of partons in n-th generation At strong coupling, branching is as fast as allowed by the uncertainty principle or Final state cannot be just a pair of partons

Medium-induced branching at finite-T Mach cone? where time-dependent drag force

Conclusion Various aspects of jets at strong coupling— including the details of the final state—are accessible from gauge/string duality techniques. Photon evolution problem sheds new light on the physics of energy loss, etc. in a strongly coupled plasma.