High Energy Scattering and StringGauge Duality

1
High Energy Scattering and String/Gauge Duality
ISMD2004, Sonoma State, California Chung-I Tan,
Brown University
Confronting String Theory with High Energy
Scattering

• Evidence for QCD as an Effective String Theory
• Maldacenas Counter Revolution Gauge/Gravity
  Duality
• Re-discovery of QCD String and Extra Dimensions
• Glueball Spectrum Hard vs Soft Pomeron in AdS
  Background
• Stretched Strings

2
QCD in Strong Coupling and HE Scattering
Some References

• Maldacena, hep-th/9711200, The Large N Limit of
  Superconformal Field Theory and Supergravity
• Brower, Mathur, Tan, hep-th/0003115, Glueball
  Spectrum for QCD from AdS Supergravity duality
• Polchinski and Strassler, hep-th/010974, Hard
  Scattering and Gauge/String Duality
  hep-th/0219211, Deep Inelastic Scattering and
  Gauge/String Duality Polchinski and Susskind,
  hep-th/0011204, String Theory and the Size of
  hadrons
• Brodsky and de Teramond, hep-th/0310227,
  Light-Front Hadron Dynamics and AdS/CFT
  Correspondence
• Brower and Tan, hep-th/0207144, Hard Scattering
  in the M-theory dual for the QCD String
• Brower, Lowe and Tan, hep-th/0211201, Hagedorn
  transition for strings on pp-wave ad tori with
  chemical potentials
• Brower and Tan, in preparation, Stretched String
  in an AdS Black hole Background and Light cone
  quantization

3
I. Evidence for QCD as String

• Asymptotic Freedom

Confinement
Force at Long Distance--Constant
Tension/Linear Potential, Coupling increasing,
Quarks and Gluons strongly bound Stringy
Behavior
4
String Modes Vibrational Modes and Rotational
Modes
5
Tests for String Excitations

• Open String Mesons
• Closed String Glueballs
• String Junction Baryons
• Open String with Fixed Sources

Phenomenological tests ISMD proceedings
last 30 years

• Can be tested using Lattice Gauge Theory
• Discrete sites --- Finite Variables Positive
  Euclidean Action --- Numerical Simulation

6
II. String/Gauge Duality

• Early String Theories Theory of Everything
• Maldacena New Era for YM Theories

7
Failure of Superstrings in Flat-Spacetime
(19731998)

• Zero mass states (gauge/graviton)
• Extra dimensions D4610
• Supersymmetries
• No Hard Scattering

8
AdS/CFT Duality (1998--)
4d YM Theories at weak coupling is dual to higher
dim String Theories with deformed AdS Background.

• Strong-Weak Dual
• Example Ising-model--(high-low temp.)
• 4d Gauge dual to Geometry in higher dim
• Absence of 4 dim-Graviton
• Wilson loop expectation sum over surfaces in
  the bulk with loop in boundary

9
Maldacenas String Counter Revolution
Open String Closed String duality
YM Wilson Loops Expectation Values in Bulk!
10
Wilson Loop in AdS/CFT
Surface into AdS space
For rectangular loop Extension into minimum
surface in r-dir
Zero Tension for QCD String--- Unacceptable
11
III. Re-discovering QCD String

• Wittens proposal---AdS/BH metric

Breaking Supersymmetry

• Deformed AdS Space, Massive Graviton
• Soft Pomeron and Tensor Glueball
• QCD String Tension

12
Witten Proposal
13
AdS/BH metric
14
VI. QCD in Strong Coupling and HE Scattering

• Stretched String--Transverse Vibrational Modes in
  deformed AdS.
• IR Physics--Glueballs as AdS Gravitons at strong
  coupling.
• UV Physics--Parton counting rules for wide-angle
  scattering.
• Stringy Deconfinement. Fat vs Thin Strings.
• Hagedorn Transition (aka deconfinement ?)
• Pomeron as Massive Graviton.
• BFKL Pomeron, Regge, DIS, Froissart Bound, ..

15
QCD after Brane Revolution
New chapter for non-perturbative QCD
Weak Coupling -- Perturbative QCD
unchanged Confinement -- Dual description in
AdS weak field approx.

• Effective degrees of freedom---massless fields of
  type IIA String theory
• Confinement by AdS/BH background

16
Physics at Different QCD Scales in AdS Space
17
Tensor Glueball/Graviton Wave functions
n1
n3
n0
r
rmin
n8
Potential
Randall-Sundram graviton
18
Glueball Spectrum
R. Brower, S. Mathur, and C-I Tan,
hep-th/0003115, Glueball Spectrum of QCD from
AdS Supergravity Duality.
19
QCD Rutherford Experiment
At WIDE ANGLES QCD exhibits power law behavior
where n åi ni is the number of partons''
in external lines.
The OPE gives
in terms of the lowest twist ti.
Actually QCD is only conformal up to small
asymptotic freedom logs.
20
Wide Angle Scattering
The 2-to-m glueball scattering amplitude
T(p1,p2,L, pm2) for plane wave glueball
scatter via the string(M-theory) amplitude A(pi,
ri, Xi) in the 10-d (or 11-d) bulk space (x,r,Y)
We now discuss two different approaches to the
QCD string that both give the correct parton
scaling formula.

• AdS5 X with IR cut-off on r rmin or 10-d IIB
  string theory
• AdS7 S4 Black Hole with horizon r rmin or
  11-d M-theory.

This is a check on the underlining universality
of Maldacena's duality conjecture.
21
10-d String theory Approach
Due to the Red Shift in the Warped Co-ordinate ,
D s (R/r) D x ,a plane wave glueball, expi x
p, scatters with a local proper momentum,
String is UV shifted in the YMs IR. (This is
the so called UV/IR connection.) THUS wide angle
scattering IS exponentially suppressed in the
region r2 rmin,rscatt
HOWEVER there is a small remaining amplitude at
large r that that gives the correct conformal
scaling of the naive parton model!
E.g for a scalar glueball f r-4 corresponding
to ni 4 for the YM operator, TrF2, in exact
agreement with the parton result.
22
Summary on Hard Scattering
(1) AdS5 Hard Scattering (Polchinski-Strassler)
WHY is it same QCD perturbative result with g2N
! (g2N)2?
(2) AdS7 Hard Scattering (Brower-Tan)
WHY does this only depend on the string tension?
(3) Compared with lowest order perturbative
results
23
string tension
AdS5, e.g. Polchinski/Strassler
AdS7 M-theory, e.g., Brower/Tan
24
Soft vs Hard Regge Scattering
Similar arguments can be applied to the Regge
limit s -t
Dominant scattering at large r, gives a BFKL-like
Pomeron with almost flat trajectory''
(actually a cut in the j-plane)
The IR region, r ' rmin, gives soft Regge pole
with slope a'qcd a' R3/r3min
The shrinkage'' of the Regge peak is caused the
soft stringy form factor'' in impact
parameter
25
Pomeron in Gauge/Gravity Duality

• Pomeron as Massive Graviton!
• Intercept lowered from 2!
• Interpolate with BFKL due to hard at AdS Bdry.

26
Stretched String in deformed AdS background

• Lattice evidence for string excitations
• Stretched String Excitations in AdS

27
M. Luscher and P. Weisz, J. H. E. Physics, 07
(2002) 328
K. J. Junge, J. Kuti, C. Morningstar,
hep-lat/0207004
28
Wilson Loop as Surface Sum
Searching for evidence of String!
29
Minimum Surface for Wilson Loop
30
QCD String a la Polyakov
31
Energy of Transverse Oscillations
Linear Potential
32
Excited states (Semi-classical limit)
At large L r0(z) ! 1, r(z) ! 1 except near end
points
r0(z) V2(z)/V2(0)
33
Radial (longitudinal) Mode

• Near r rmin (or y 0), V(y) ' r2min const
  y2

THE SPECTRUM IS GAUGE INVARIANT

• Choose a gauge with fluctuations only in
  longitudinal (X3) or radial (Y) or normal to
  classical surface, etc
• X3 z x or Y
  ycl(z) x , etc

except at end points
D E (d1) MGB O(1/L)
34
V. Future Developments

• Improved Confining Background
• Challenges BFKL, Froissart bound, Massless
  Quarks, Chiral Symmetry, ..
• ..
• Beyond strong coupling or Strong Gravity.

See you at next ISMD!