Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops

Abstract

We calculate form factors of half-BPS operators in N=4 super Yang-Mills theory at tree level and one loop using novel applications of recursion relations and unitarity. In particular, we determine the expression of the one-loop form factors with two scalars and an arbitrary number of positive-helicity gluons. These quantities resemble closely the MHV scattering amplitudes, including holomorphicity of the tree-level form factor, and the expansion in terms of two-mass easy box functions of the one-loop result. Next, we compare our result for these form factors to the calculation of a particular periodic Wilson loop at one loop, finding agreement. This suggests a novel duality relating form factors to periodic Wilson loops.

26 pages, 10 figures. v2: typos fixed, comments added

References in corpus (11)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Form factors at strong coupling via a Y-system
• Analytic Results for MHV Wilson Loops
• Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling
• A Surprise in the Amplitude/Wilson Loop Duality

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