Four-loop four-point correlator integrand in planar N=4 SYM decomposes into chamber forms identical to three loops times local integrands, with leading singularities as linear combinations of those forms and a diagonalized pure-function representation including one pure elliptic integrand.
A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
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abstract
We prove that in the limit when its insertion points become pairwise null-separated, the ratio of certain n-point correlation functions in N=4 SYM is equal to a supersymmetric Wilson loop on twistor space, acting in the adjoint representation. In the planar limit, each of these objects reduces to the square of the complete n-particle planar superamplitude. Our proof is at the level of the integrand.
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Leading singularities and chambers of Correlahedron
Four-loop four-point correlator integrand in planar N=4 SYM decomposes into chamber forms identical to three loops times local integrands, with leading singularities as linear combinations of those forms and a diagonalized pure-function representation including one pure elliptic integrand.