Cluster adjacency properties of scattering amplitudes

We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalise the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. We study heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.Comment: 6 pages, 3 figures. Symbols of integrals presented in four ancillary files, as detailed in README.tx

Cluster adjacency beyond MHV

We explore further the notion of cluster adjacency, focussing on non-MHV amplitudes. We extend the notion of adjacency to the BCFW decomposition of tree-level amplitudes. Adjacency controls the appearance of poles, both physical and spurious, in individual BCFW terms. We then discuss how this notion of adjacency is connected to the adjacency already observed at the level of symbols of scattering amplitudes which controls the appearance of branch cut singularities. Poles and symbols become intertwined by cluster adjacency and we discuss the relation of this property to the $\bar{Q}$-equation which imposes constraints on the derivatives of the transcendental functions appearing in loop amplitudes.Comment: 51 pages, 25 figures, 4 table

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Editorial

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Letter from Jack Foster Ellard to Pauline Smith; February 23, 1942

From the Ellard-Murphree-Pilgreen-Smith Family Papers Collection. Letter from Jack Foster Ellard to Pauline Smith; February 23, 1942. Foss tells Pauline about his military life, updating her on his work and sharing that he has been recommended to be a Commander, as well as a deacon at his church. He has a new renter at his house who he is trying to set up with Christine, and expresses his worry about John Allen Jr., who is still a prisoner of war.https://athenacommons.muw.edu/smithpapers/1183/thumbnail.jp