Related papers: Cancellation of spurious poles in N=4 SYM: physica…
We consider tree level form factors of operators from stress tensor operator supermultiplet with light-like operator momentum $q^2=0$. We present a conjecture for the Grassmannian integral representation both for these tree level form…
A basis shape locus takes as input data a zero/nonzero pattern in an $n \times k$ matrix, which is equivalent to a presentation of a transversal matroid. The locus is defined as the set of points in the Grassmannian of $k$ planes in…
This note addresses the problem of spurious poles in gauge-theoretic scattering amplitudes. New twistor coordinates for the momenta are introduced, based on the concept of dual conformal invariance. The cancellation of spurious poles for a…
This article proves the cyclicity of anti-NMHV and N$^2$MHV tree amplitudes in planar N=4 SYM up to any number of external particles as an interesting application of positive Grassmannian geometry. In this proof the two-fold simplex-like…
We incorporate all gauge-invariant local composite operators into the twistor-space formulation of N=4 SYM theory, detailing and expanding on ideas we presented recently in arXiv:1603.04471. The vertices for these operators contain…
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 derive an on-shell diagram recursion for tree-level scattering amplitudes in $\mathcal{N}=7$ supergravity. The diagrams are evaluated in terms of Grassmannian integrals and momentum twistors, generalising previous results of Hodges in…
In this paper, we study a new application of the positive Grassmanian to Wilson loop diagrams (or MHV diagrams) for scattering amplitudes in N=4 Super Yang-Mill theory ($N=4$ SYM). There has been much interest in studying this theory via…
A positroid is the matroid of a real matrix with nonnegative maximal minors, a positroid variety is the closure of the locus of points in a complex Grassmannian whose matroid is a fixed positroid, and a positroid class is the cohomology…
Given an embedded smooth projective variety Y in CP^n, we show how the existence of a hypersurface with high multiplicity along Y, but of relatively low degree and log canonical near Y implies vanishing of higher cohomology for certain…
We initiate an exploration of on-shell functions in $\mathcal{N}=4$ SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHV amplitudes and showing that they can always be expressed as…
Inspired by the idea of viewing amplitudes in ${\cal N}=4$ SYM as differential forms on momentum twistor space, we introduce differential forms on the space of spinor variables, which combine helicity amplitudes in any four-dimensional…
This article revisits and elaborates the significant role of positive geometry of momentum twistor Grassmannian for planar N=4 SYM scattering amplitudes. First we establish the fundamentals of positive Grassmannian geometry for tree…
In this paper we explore the geometric space parametrized by (tree level) Wilson loops in SYM $N=4$. We show that, this space can be seen as a vector bundle over a totally non-negative subspace of the Grassmannian, $\mathcal{W}_{k,cn}$.…
We perform the twistor (half-Fourier) transform of all tree n-particle superamplitudes in N=4 SYM and show that it has a transparent geometric interpretation. We find that the N^kMHV amplitude is supported on a set of (2k+1) intersecting…
Matroid varieties are the closures in the Grassmannian of sets of points defined by specifying which Pl\"ucker coordinates vanish and which don't. In general these varieties are very ill-behaved, but in many cases one can estimate their…
Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests…
We show that 4-point vector boson one-loop amplitudes, computed in ref.[1] in the RNS formalism, around vacuum configurations with open unoriented strings, preserving at least N=1 SUSY in D=4, satisfy the correct supersymmetry Ward…
We elaborate the two-fold simplex-like structures of tree amplitudes in planar maximally supersymmetric Yang-Mills (N=4 SYM), through its connection to a mathematical structure known as the positive Grassmannian. Exploiting the reduced…
We construct a complex of toric varieties we call the quasisymmetric Grassmannian inside the Grassmannian of $r$-planes in $\mathbb{C}^n$. Each irreducible component is a positroid variety and an $S_n$ translate of a toric Richardson…