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A bstract Colorfactor symmetry is a property of treelevel gaugetheory amplitudes containing at least one gluon. BCJ relations among colorordered amplitudes follow directly from this symmetry. Colorfactor symmetry is also a feature of biadjoint scalar theory amplitudes as well as of their equations of motion. In this paper, we present a new proof of colorfactor symmetry using a recursive method derived from the perturbiner expansion of the classical equations of motion.more » « less

A bstract A previously proposed alllooporders relation between the Regge limits of fourpoint amplitudes of $$ \mathcal{N} $$ N = 4 supersymmetric YangMills theory and $$ \mathcal{N} $$ N = 8 supergravity is established at the threeloop level. We show that the Regge limit of known expressions for the amplitudes obtained using generalized unitarity simplifies in both cases to a (modified) sum over threeloop ladder and crossedladder scalar diagrams. This in turn is consistent with the result obtained using the eikonal representation of the fourpoint gravity amplitude. A possible exact threeloop relation between fourpoint amplitudes is also considered.more » « less

null (Ed.)A bstract We examine in detail the structure of the Regge limit of the (nonplanar) $$ \mathcal{N} $$ N = 4 SYM fourpoint amplitude. We begin by developing a basis of color factors C ik suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through threeloop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through $$ \mathcal{O}\left({\upepsilon}^2\right) $$ O ϵ 2 at two loops, and through $$ \mathcal{O}\left({\upepsilon}^0\right) $$ O ϵ 0 at three loops, verifying that the IRdivergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the threeloop correction to the dipole formula. We also verify consistency with the IRfinite NLL and NNLL predictions of CaronHuot et al. Finally we use these results to motivate the conjecture of an allorders relation between one of the coefficients and the Regge limit of the $$ \mathcal{N} $$ N = 8 supergravity fourpoint amplitude.more » « less