new perspective for qcd: string /gauge duality evidence for qcd as an effective string theory...
TRANSCRIPT
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New Perspective for QCD: String/Gauge Duality
• Evidence for QCD as an Effective String Theory• Maldacena’s Counter Revolution: Gauge/Gravity Duality• Re-discovery of QCD String and Extra Dimensions • QCD in Strong Coupling: Hard vs Soft Pomeron in AdS
Background
Confronting String Theory with High Energy ScatteringConfronting String Theory with High Energy Scattering
Small-x and Diffraction, FNAL, 2003----Chung-I Tan, Brown
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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 <==> “Stringy Behavior”
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String Modes: Vibrational Modes and Rotational Modes
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Tests for String Excitations• Open String <===> Mesons• Closed String <===> Glueballs• String Junction <===> Baryons
• Open String with Fixed Sources
Can be tested using Lattice Gauge Theory:
Discrete sites ---> Finite Variables Positive Euclidean Action ---> Numerical Simulation
Phenomenological tests <====> Moriond proceedings last 30 years
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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 ==> 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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Luscher’s Conclusion
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II. String/Gauge Duality
Early String Theories ==> Theory of Everything
Maldacena ==> 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 (1973~1998)
• Zero mass states: (gauge/graviton)
• Extra dimensions: D=4+6=10
• Supersymmetries:
• No Hard Scattering:
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AdS/CFT Duality (1998--)
• 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
4d YM Theories at weak coupling is dual to higher dim String Theories with deformed AdS Background.
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Maldacena’s String Counter Revolution
Open String <=====> Closed String
dualityYM Wilson Loops <---> Expectation Values in Bulk!
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Minor Problem: Wilson Loop in AdS/CFT
For rectangular loop: Extension into minimum surface in r-dir
Surface into AdS space
Zero Tension for QCD String---> Unacceptable
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III. Re-discovering QCD String
Witten’s proposal---AdS/BH metric
•Deformed AdS Space, Massive Graviton•Soft Pomeron and Tensor Glueball•QCD String Tension
Breaking Supersymmetry
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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
• Effective degrees of freedom---massless fields of type IIA String theory
• Confinement by AdS/BH background
New chapter for non-perturbative QCD
Weak Coupling --> Perturbative QCD : unchanged
Confinement --> Dual description in AdS : weak field approx.
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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
n=1 n=3
n=8 Potential
n=0
Randall-Sundram gravitonrmin
r
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QCD Rutherford Experiment
At WIDE ANGLES QCD exhibits power law behavior:
where n= i ni is the number of ``partons'' in external lines.
Actually QCD is only conformal up to small asymptotic freedom logs.
The OPE gives
in terms of the lowest twist i.
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Wide Angle ScatteringThe 2-to-m glueball scattering amplitude T(p1,p2,L, pm+2) for plane wave glueball:
This is a check on the underlining universality of Maldacena's duality conjecture.
scatter via the string(M-theory) amplitude: A(pi, ri, Xi) in the 10-d (or 11-d) bulk space (x,r,Y):
• 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.
We now discuss two different approaches to the QCD string that both give thecorrect parton scaling formula.
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10-d String theory ApproachDue to the Red Shift in the Warped Co-ordinate , s = (R/r) x ,a plane wave glueball, exp[i x p], scatters with a local proper momentum,
String is UV shifted in the YM’s 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 » r-4 corresponding to ni = 4 for the YM operator, Tr[F2], in exact agreement with the parton result.
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Summary on Hard Scattering
(3) Compared with lowest order perturbative results:
(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?
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Soft vs Hard Regge ScatteringSimilar 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 'qcd » ' 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!