Wilson Loops and QCD/String Scattering Amplitudes

Abstract

We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in $\mathcal{N}=4$ SYM to large $N$ QCD by deriving a general relation between QCD meson scattering amplitudes and Wilson loops. We then investigate properties of the open-string disk amplitude integrated over reparametrizations. When the Wilson loop is approximated by the area behavior, we find that the QCD scattering amplitude is a convolution of the standard Koba-Nielsen integrand and a kernel. As usual poles originate from the first factor, whereas no (momentum dependent) poles can arise from the kernel. We show that the kernel becomes a constant when the number of external particles becomes large. The usual Veneziano amplitude then emerges in the kinematical regime where the Wilson loop can be reliably approximated by the area behavior. In this case we obtain a direct duality between Wilson loops and scattering amplitudes when spatial variables and momenta are interchanged, in analogy with the $\mathcal{N}$=4 SYM case.

39pp., Latex, no figures; v2: typos corrected; v3: final, to appear in PRD

References in corpus (8)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• On planar gluon amplitudes/Wilson loops duality
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• The closed string spectrum of SU(N) gauge theories in 2+1 dimensions
• Universality of large N phase transitions in Wilson loop operators in two and three dimensions
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Cited by in corpus (19)

• Remarks on Holographic Wilson Loops and the Schwinger Effect
• More about One-Loop Effective Action of Open Superstring in $Ad{S}_5\times S^5$
• The QCD scattering amplitude from area behaved Wilson loops
• Lightlike contours with fermions
• Quantum corrections from a path integral over reparametrizations
• Effective String Theory and QCD Scattering Amplitudes
• An interplay between static potential and Reggeon trajectory for QCD string
• Path Integral over Reparametrizations: Levy Flights versus Random Walks
• Holographic Corrections to Meson Scattering Amplitudes
• Semiclassical Regge trajectories of noncritical string and large-N QCD
• Large-N QCD and the Veneziano Amplitude
• Holographic Corrections to the Veneziano Amplitude
• Scattering amplitudes of regularized bosonic strings
• Equivalence of Meson Scattering Amplitudes in Strong Coupling Lattice and Flat Space String Theory
• Scattering Amplitudes of QCD String
• Large-size expansion for triangular Wilson loops in confining gauge theories
• Asymptotic behavior of large polygonal Wilson loops in confining gauge theories
• Worldsheets in Holography: Computing Corrections to the Veneziano Amplitude
• Comments on open string with "massive" boundary term