Related papers: Positive and Negative Ladders in Loop Space

Scattering amplitudes in $D$ dimensions involve particular terms that originate from the interplay of UV poles with the $D-4$ dimensional parts of loop numerators. Such contributions can be controlled through a finite set of…

We study massive one-loop integrals by analytically continuing the Feynman integral to negative dimensions as advocated by Halliday and Ricotta and developed by Suzuki and Schmidt. We consider n-point one-loop integrals with arbitrary…

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…

We present a compact analytic formula for the two-loop six-particle MHV remainder function (equivalently, the two-loop light-like hexagon Wilson loop) in N = 4 supersymmetric Yang-Mills theory in terms of the classical polylogarithm…

Form factors of the stress-tensor multiplet operator in $\mathcal{N}=4$ supersymmetric Yang-Mills reveal surprisingly simple structures similar to those appearing in scattering amplitudes. In this paper we show that, as for the case of…

In this paper we study the combinatorics associated with the positive orthogonal Grassmannian OG_k and its connection to ABJM scattering amplitudes. We present a canonical embedding of OG_k into the Grassmannian Gr(k,2k), from which we…

We extend the hexagon function bootstrap to the next-to-maximally-helicity-violating (NMHV) configuration for six-point scattering in planar ${\cal N}=4$ super-Yang-Mills theory at three loops. Constraints from the $\bar{Q}$ differential…

We consider the duality between the four-dimensional S-matrix of planar maximally supersymmetric Yang-Mills theory and the expectation value of polygonal shaped Wilson loops in the same theory. We extend the duality to amplitudes with…

Second-order ordinary linear differential equations appear ubiquitously across physics, describing the behavior of systems from the quantum world of atoms to the classical world of gravitating bodies. We present a unified symmetry-based…

We consider scattering amplitudes in planar N = 4 supersymmetric Yang-Mills theory in special kinematics where all external four-dimensional momenta are restricted to a (1+1)-dimensional subspace. The amplitudes are known to satisfy…

Carrollian amplitudes are scattering amplitudes of massless particles written in position space at null infinity. We study various aspects of Carrollian amplitudes for gauge theory and gravity at loop level using primarily the modified…

Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…

We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N=4 super-Yang-Mills theory. We provide exact, finite-coupling…

It is widely expected that NMHV amplitudes in planar, maximally supersymmetric Yang-Mills theory require symbol letters that are not rationally expressible in terms of momentum-twistor (or cluster) variables starting at two loops for eight…

We construct the six-point NMHV one-loop amplitude in ${\cal N}=4$ supergravity using unitarity and recursion. The use of recursion requires the introduction of rational descendants of the cut-constructible pieces of the amplitude and the…

We advance the exploration of cluster-algebraic patterns in the building blocks of scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills theory. In particular we conjecture that, given a maximal cut of a loop amplitude, Landau…

Building on the prior work in [1] we locate a family of positive geometries in the kinematic space which are a specific class of convex realisations of the associahedron. These realisations are obtained by scaling and translating the…

We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N=4 super Yang-Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N=4 super Yang-Mills are used as vertices, using…

Given a dilation matrix M, a so-called space of M-positive vectors in the Euclidean space is introduced and studied. An algebraic structure of this space is similar to the positive half-line equipped with the termwise addition modulo 2,…

The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This…