jets in n=4 sym from ads/cft
DESCRIPTION
Jets in N=4 SYM from AdS/CFT. Yoshitaka Hatta U. Tsukuba. Y.H., E. Iancu, A. Mueller, arXiv:0803.2481 [hep-th] (JHEP) Y.H., T. Matsuo, arXiv:0804.4733 [hep-th]. Contents. Introduction e^+e^- annihilation and Jets in QCD Jet structure at strong coupling Jet evolution at finite temperature. - PowerPoint PPT PresentationTRANSCRIPT
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Jets in N=4 SYM from AdS/CFT
Yoshitaka HattaU. Tsukuba
Y.H., E. Iancu, A. Mueller, arXiv:0803.2481 [hep-th] (JHEP)Y.H., T. Matsuo, arXiv:0804.4733 [hep-th]
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Contents
Introduction e^+e^- annihilation and Jets in QCD Jet structure at strong coupling Jet evolution at finite temperature
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Strongly interacting matter at RHIC
Observed jet quenching of high-pt hadrons is stronger than pQCD predictions.
dypd
dN
coll
dypd
dN
AA
T
pp
T
AA
NR
2
2
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Strongly interacting matter at RHIC
Ideal hydro simulation works,suggesting short mean free path.
2cos)(21 2 Tpvd
dn
low viscosity, strong jet quenching
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The Regge limit of QCD
tot 08.0ss2ln
Hadron-hadron total cross section grows with energy (‘soft Pomeron’)
c.f., pQCD prediction (BFKL, ‘hard Pomeron’)
ss 2ln4
or
?
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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:0801.0629 [hep-ph]
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Deep inelastic scattering in QCD
P X
e
2Q
222
22
2 Qmm
Q
qP
Q
pX
x
x
Two independent kinematic variables
22 Qq Photon virtuality
Bjorken-
Momentum fraction of a parton
),( 2QxDS : Parton distribution function Count how many partons are there inside a proton.
2122
,)(),(ln
Qz
xDzP
z
dzQxD
Q SSxSDGLAP equation
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DIS vs. e^+e^- annihilation
P
e 022 Qq
e
022 Qq
e
Bjorken variable Feynman variable
P
qP
Qx
2
2
2
2
Q
qPx
Parton distribution function Fragmentation function
),( 2QxDS),( 2QxDT
crossing
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Jets in QCD
ee
Average angular distributionreflecting fermionic degrees of freedom (quarks)
2cos1
Observation of jets in `75 provides one of the most striking confirmations of QCD
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Fragmentation function
ee
P Count how many hadrons are there inside a quark.
),( 2QxDT
Q
E
Q
qPx 222
Feynman-x
First moment
nQxDdx T ),( 21
0 average multiplicity
2),( 21
0 QxxDdx T energy conservation
Second moment
022 Qq
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Evolution equation
The fragmentation functions satisfy a DGLAP-type equation
),()(),(ln
222
QjDjQjDQ TTT
),(),( 211
0
2 QxDxdxQjD Tj
TTake a Mellin transform
Timelike anomalous dimension
)1(22 ),1( TQQDn T (assume )0
2122
,)(),(ln
Qz
xDzP
z
dzQxD
Q TTxT
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Anomalous dimension in QCDLowest order perturbation
Soft singularity
~x
11
)(
j
j sT
!!)1( T
ResummationAngle-ordering
)1(
8)1(
4
1)( 2 j
Njj s
T
Mueller, `81
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Inclusive spectrum
largel-x small-x
x1ln
),( 2QxxDdx
dxT
roughly an inverse Gaussian peaked at
Q
x
1
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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.
0CYM Ng 2
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Type IIB superstring
Consistent superstring theory in D=10 Supergravity sector admits the black 3-bra
ne solution which is asymptotically
Our universe
5S
AdS `radius’ coordinate
55 SAdS
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(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
CN CYM Ng 2
Maldacena, `97
2'4 RCN1 sg
CFT string
55 SAdS
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Dilaton localized at small
DIS at strong coupling
R-charge current excites metric fluctuations in the bulk, which then scatters off a dilaton (`glueball’)
r
r
Cut off the space at (mimic confinement)
022 Qq
Polchinski, Strassler, `02Y.H. Iancu, Mueller, `07
We are here
Photon localized at large Qr
0rr
)( r
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e^+e^- annihilation at strong coupling
Hofman, MaldacenaY.H., Iancu, Mueller,Y.H. Matsuo
arXiv:0803.1467 [hep-th]arXiv:0803.2481 [hep-th]arXiv:0804.4733 [hep-th]
022 Qq
5D Maxwell equation
Dual to the 4D R-current
)(2
1)(
2
1)( 433465562211 DDDDxJ
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A reciprocity relation
),()(),(ln
2//
2/2
QjDjQjDQ TSTSTS
DGRAP equation
Dokshitzer, Marchesini, Salam, ‘06
The two anomalous dimensions derive from a single function
Basso, Korchemsky, ‘07Application 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
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Anomalous dimension in N=4 SYM
Gubser, Klebanov, Polyakov, `02
)(22
1
2)( 0jj
jjS 2j Kotikov, Lipatov, Onishchenko, Velizhanin `05
Brower, Polchinski, Strassler, Tan, `06
)(22 jj S
2~j
jj XXrV
Leading Regge trajectory Twist—two operators
lowest mass state for given j lowest dimension operator for given j
The `cusp’ anomalous dimension
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Average multiplicity
)(22
1
2)( 0jj
jjS
22
1)(
2
0
jjjjT
231)1(2)( QQQn T
c.f. in perturbation theory, 22)(
QQn
crossing
c.f. heuristic argument QQn )( Y.H., Iancu, Mueller ‘08
Y.H., Matsuo ‘08
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Jets at strong coupling?
The inclusive distribution is peaked at the kinematic lower limit
1QQEx 2
QxFQQxDT
22 ),(
Rapidly decaying function for Qx
21)(
jjT in the supergravity limit
At strong coupling, branching is so fast and efficient. There are no partons at large-x !
Q
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Energy correlation functionHofman, Maldacena `08
Energy distribution is spherical for anyCorrelations disappear as
QAll the particles have the minimal four momentum~ and are spherically emitted. There are no jets at strong coupling !
1)()3( OS
241 weak coupling
strong coupling
1
2
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Evolution of jets in a N=4 plasmaY.H., Iancu, Mueller `08
Solve the Maxwell equation
in the background of Schwarzschild AdS_5
25
2244
02
222
4
40
2
22
)1()(1
dRdr
rrr
Rxddt
r
r
R
rds
TRr 20
)(),,( rAerxtA iqzti
To compute correlation functions :2222 TQq
r
0rr Event horizon
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Time-dependent Schrödinger equation
2
,2 0
r
r
Solutions available only piecewise.Qualitative difference between
t=0
horizon
Tk
2
312 )( TQQ s sQQ
Minkowskiboundary
‘low energy’ and ‘high energy’
T
QK
2
sQ : plasma saturation momentum
),(),,( rtAerxtA iqzti
To study time-evolution, add a weak t-dependence and keep only the 1st t-derivative
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low-energy,
Early time diffusion
AV BV CV
solution with AV
This represents diffusion
up to time || 2Q
qt
312 )(qTQQ s
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Gauge theory interpretation
IR/UV correspondence
TLr
r 02
L Q1
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)|| 2Q
qt
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low-energy
Intermediate free streaming region
AV BV CV
solution with BV
constant (group-) velocity motion
tq
Q
312 )(qTQQ s
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Gauge theory interpretation
IR/UV correspondence
Q1
21 zvq
Q is the transverse velocity
tvL T2
Lq
Q
T
1
TL Linear expansion of the pair
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low-energy
Falling down the potential
AV BV CV
solution with CV
A classical particle with mass falling down the potential
k
312 )(qTQQ s
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Gauge theory interpretation
Q1 q
Q
T
1T
1
disappear into the plasma
Tp ||
start to `feel’ the plasma
In-medium acceleration
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The high energy case
AV BV CV
312 )(qTQQ s
A new characteristic time
22 Q
q
Q
qt
s
sQ1T
1
No difference between the timelike/spacelike cases
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The scale
is the meson screening length
Energy loss, meson screening length, and all that
T
v
q
Q
TL z
412 )1(1
Liu, Rajagopal, Wiedemann, `06 Q1q
Q
T
1
WKP solution after the breakup features the trailing string solution
))((exp rtvziq z
00
0 arctanln2
1)(
r
r
rr
rr
Tr
Herzog, et al, ‘06, Gubser, ‘06
breakup
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Energy loss, meson screening length,and all that
Rate of enery flow towards the horizon
Identical to the motion of our wavepacket
312
qt
sf
sQ1T
1 Time to reach the horizon
ftc.f., damping time of a gluon
31qGubser, Gulotta, Pufu, Rocha, 0803.1470 [hep-th]
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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
nn
2
nn
2
221 2Q
q
Q
qtt n
n
nnn
QQn )(
,1)( ttQ or ttL )(
Final state cannot be just a pair of partons
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Medium-induced branching at finite-T
Mach cone?
)(221ns
n
n
nnn qQ
q
Q
qtt
22 )()()(
TttQdt
tdqs where
31
T
q
Q
q
s
time-dependent drag force
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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.