Related papers: Adjacency for scattering amplitudes from the Gr\"o…
There is a remarkable well-known connection between the G$(4,n)$ cluster algebra and $n$-particle amplitudes in $\mathcal{N}=4$ SYM theory. For $n \ge 8$ two long-standing open questions have been to find a mathematically natural way to…
We initiate the study of cluster algebras in Feynman integrals in dimensional regularization. We provide evidence that four-point Feynman integrals with one off-shell leg are described by a $C_{2}$ cluster algebra, and we find cluster…
Recent years have seen the emergence of a new understanding of scattering amplitudes in the simplest theory of colored scalar particles - the Tr$(\phi^3)$ theory - based on combinatorial and geometric ideas in the kinematic space of…
All-loop planar scattering amplitudes in maximally supersymmetric Yang-Mills theory can be formulated geometrically in terms of the "amplituhedron". We study the mathematical structures of the one-loop amplituhedron, and present a new…
Symbol alphabets of n-particle amplitudes in N=4 super-Yang-Mills theory are known to contain certain cluster variables of Gr(4,n) as well as certain algebraic functions of cluster variables. The first paper arXiv:2007.00646 in this series…
We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of $n$ massless particles are given…
We review recent progress on computing scattering amplitudes of planar N=4 super Yang-Mills at strong coupling by using the AdS/CFT duality. We do explicit computations by using both, dimensional regularization and a cut-off in the radial…
In [arXiv:1906.10100], the authors argued that the Newman-Janis algorithm on the space of classical solutions in general relativity and electromagnetism could be used in the space of scattering amplitudes to map an amplitude with external…
Momentum twistors for scattering amplitudes in particle physics are lines in three-space. We develop Landau analysis for Feynman integrals in this setting. The resulting discriminants and resultants are identified with Hurwitz and Chow…
Motivated by reformulating Yangian invariants in planar ${\cal N}=4$ SYM directly as $d\log$ forms on momentum-twistor space, we propose a purely algebraic problem of determining the arguments of the $d\log$'s, which we call "letters", for…
Attached to both Yang-Mills and General Relativity about Minkowski spacetime are distinguished gauge independent objects known as the on-shell tree scattering amplitudes. We reinterpret and rigorously construct them as $L_\infty$ minimal…
We investigate a new algebra-based approach of finding Grassmannian formulas for scattering amplitudes. Our prime motivation is massive amplitudes of 4D $\mathcal{N}=4$ SYM, and therefore we consider a 6D Grassmannian formula, where we can…
Perturbatively around flat space, the scattering amplitudes of gravity are related to those of Yang-Mills by colour-kinematic duality, under which gravitational amplitudes are obtained as the 'double copy' of the corresponding gauge theory…
We compute the leading-color (planar) three-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4 - 2 epsilon dimensions, as a Laurent expansion about epsilon = 0 including the finite terms. The amplitude was constructed…
It is shown that the four-gluon scattering amplitude for N=4 supersymmetric Yang-Mills theory in the planar limit can be written, in both the weak- and strong-coupling limits, as a reggeized amplitude, with a parent trajectory and an…
The Pl\"ucker positive region $\mathrm{OGr}_+(k,2k)$ of the orthogonal Grassmannian emerged as the positive geometry behind the ABJM scattering amplitudes. In this paper we initiate the study of the positive orthogonal Grassmannian…
Matrix Schubert varieties are the closures of the orbits of $B\times B$ acting on all $n\times n$ matrices, where $B$ is the group of invertible lower triangular matrices. Extending work of Fulton, Knutson and Miller identified a Gr\"obner…
We review various aspects of cluster algebras and the ways in which they appear in the study of loop-level amplitudes in planar ${\cal N} = 4$ supersymmetric Yang-Mills theory. In particular, we highlight the different forms of…
We study the geometry underlying the Wilson loop diagram approach to calculating scattering amplitudes in the gauge theory of Supersymmetric Yang Mills (SYM) $N=4$. By applying the tools developed to study total positivity in the real…
We study scattering amplitudes and form factors in planar $\mathcal{N}=4$ Super Yang-Mills theory in the limit where two pairs of gluons become collinear. We find that, when the virtualities of both collinear pairs are spacelike, the…