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Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
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abstract
We compute the symbol of the first two-loop amplitudes in planar ${\cal N}=4$ SYM with algebraic letters, the eight-point NMHV amplitude (or the dual octagon Wilson loops). We show how to apply $\bar{Q}$ equations for computing the differential of two-loop $n$-point NMHV amplitudes and present the result for n=8 explicitly. The symbol alphabet for octagon consists of 180 independent rational letters and 18 algebraic ones involving Gram-determinant square roots. We comment on all-loop predictions for final entries and aspects of the result valid for all multiplicities.
Forward citations
Cited by 3 Pith papers
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Cluster Algebras, Cube Roots, and Energy Correlators in $\mathcal{N}=4$ SYM
Infinite mutation sequences of the cluster quiver Q3 generate the six cubic algebraic symbol letters of the near-collinear four-point energy correlator in N=4 super-Yang-Mills theory.
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Double spacelike collinear limits from multi-Regge kinematics
The double spacelike collinear limit of planar N=4 SYM is governed by a generalized splitting amplitude that equals the six-point BDS-subtracted amplitude in multi-Regge kinematics.
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Hexagonal Wilson loop with Lagrangian insertion at two loops in $\mathcal{N}=4$ super Yang-Mills theory
The two-loop symbol for the hexagonal Wilson loop with a Lagrangian insertion in planar N=4 super Yang-Mills theory is uniquely fixed by a symbol bootstrap and satisfies the expected Steinmann relations.
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