Duality between Wilson loops and gluon amplitudes

Abstract

An intriguing new duality between planar MHV gluon amplitudes and light-like Wilson loops in N=4 super Yang-Mills is investigated. We extend previous checks of the duality by performing a two-loop calculation of the rectangular and pentagonal Wilson loop. Furthermore, we derive an all-order broken conformal Ward identity for the Wilson loops and analyse its consequences. Starting from six points, the Ward identity allows for an arbitrary function of conformal invariants to appear in the expression for the Wilson loop. We compute this function at six points and two loops and discuss its implications for the corresponding gluon amplitude. It is found that the duality disagrees with a conjecture for the gluon amplitudes by Bern et al. A recent calculation by Bern et al indeed shows that the latter conjecture breaks down at six gluons and at two loops. By doing a numerical comparison with their results we find that the duality between gluon amplitudes and Wilson loops is preserved. This review is based on the author's PhD thesis and includes developments until May 2008.

102 pages, based on the author's PhD thesis

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• Bootstrapping the three-loop hexagon
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• Exacting N=4 Superconformal Symmetry
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• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• New differential equations for on-shell loop integrals
• More loops and legs in Higgs-regulated N=4 SYM amplitudes
• On BCFW shifts of integrands and integrals
• No triangles on the moduli space of maximally supersymmetric gauge theory
• Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory
• Simple loop integrals and amplitudes in N=4 SYM
• SL(2) sector: weak/strong coupling agreement of three-point correlators
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• Dual conformal symmetry at loop level; massive regularization
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• Three-point functions in planar N=4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order
• Correlation function of null polygonal Wilson loops with local operators
• Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes
• Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory
• Three-Point Functions of Twist-Two Operators in N=4 SYM at One Loop
• One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• Scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills
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• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• A Celestial Description of Planar Super-Yang-Mills Theory
• Wilson Loops and Integrability
• N=4 Supersymmetric Yang-Mills theory in soft-collinear effective theory