New Perspective for QCD: String/Gauge Duality

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New Perspective for QCD String/Gauge Duality
Small-x and Diffraction, FNAL, 2003----Chung-I
Tan, Brown
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
• QCD in Strong Coupling Hard vs Soft Pomeron in
  AdS Background

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I. Evidence for QCD as String

• Asymptotic Freedom

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

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

Phenomenological tests ltgt Moriond
proceedings last 30 years

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

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Wilson Loop as Surface Sum
Searching for evidence of String!
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Recent Results of Martin Luscher et al.

• String Excitation Energies can be measured by
  Wilson Loop Correlation function,
• Precision measurement gt effective bosonic
  string.
• Further structure yet to be understood.

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M. Luscher and P. Weisz, J. H. E. Physics, 07
(2002) 328
K. J. Junge, J. Kuti, C. Morningstar,
hep-lat/0207004
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Luschers Conclusion
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II. String/Gauge Duality

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

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How Can QCD be a String Theory? Topological
Expansion
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Failure of Superstrings in Flat-Spacetime
(19731998)

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

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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

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Maldacenas String Counter Revolution
Open String ltgt Closed String duality
YM Wilson Loops lt---gt Expectation Values in Bulk!
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Minor Problem Wilson Loop in AdS/CFT
Surface into AdS space
For rectangular loop Extension into minimum
surface in r-dir
Zero Tension for QCD String---gt Unacceptable
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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

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Witten Proposal
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AdS/BH metric
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Minimum Surface for Wilson Loop
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M. Luscher and P. Weisz, J. H. E. Physics, 07
(2002) 328
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VI. QCD in Strong Coupling and HE Scattering

• 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, ..

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

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

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Glueball Spectrum
R. Brower, S. Mathur, and C-I Tan,
hep-th/0003115, Glueball Spectrum of QCD from
AdS Supergravity Duality.
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Pomeron in Gauge/Gravity Duality

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

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Physics at Different QCD Scales in AdS Space
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Tensor Glueball/Graviton Wave functions
n1
n3
n0
r
rmin
n8
Potential
Randall-Sundram graviton
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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.
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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 gt 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.
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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.
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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
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Soft vs Hard Regge Scattering
Similar arguments can be applied to the Regge
limit s gtgt -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
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V. Future Developments

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

See you at next FNAL Small-x Meeting!