Related papers: Cross-Order Integral Relations from Maximal Cuts

We review recent progress in D-dimensional integrand reduction algorithms for two loop amplitudes and give examples of their application to non-planar maximal cuts of the five-point all-plus helicity amplitude in QCD.

We systematically classify all possible poles of superconformal blocks as a function of the scaling dimension of intermediate operators, for all superconformal algebras in dimensions three and higher. This is done by working out the…

We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general…

A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different…

One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators…

We use the recently developed generalized double-copy procedure to construct an integrand for the five-loop four-point amplitude of N=8 supergravity. This construction starts from a naive double copy of the previously computed corresponding…

Higher order coefficients of the inverse mass expansion of one--loop effective actions are obtained from a one--dimensional path integral representation. For the evaluation of the path integral with Wick contractions a suitable Green…

We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived…

We present a set of algebraic functions for evaluating the coefficients of the scalar integral basis of a general one-loop amplitude. The functions are derived from unitarity cuts, but the complete cut-integral procedure has been carried…

The existence of decompositions of the nonlinear integrable systems not only permits us to establish so-called linear superposition solutions but also to derive new nonlinear integrable coupled systems. Restricting our attention to the…

Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…

We establish necessary and sufficient conditions for the existence of a decomposition of a complete multigraph into edge-disjoint cycles of specified lengths, or into edge-disjoint cycles of specified lengths and a perfect matching.

We present analytical results for one-loop five-point master integrals with up to three off-shell legs. The method of canonical differential equations along with the Simplified Differential Equations approach is employed. All necessary…

We derive the structure of three-loop anomalous dimensions governing infrared singularities of QCD amplitudes with one massive and an arbitrary number of massless external partons. The contributions of tripole and quadrupole correlations…

We advertise intersection theory for generalised hypergeometric functions as a means of evaluating Mellin-Barnes representations. As an example, we study two-parameter representations of the off-shell one- and two-loop box graphs in exactly…

We perform a comprehensive perturbative study of the operator spectrum in multi-scalar theories with hypercubic global symmetry. This includes working out symmetry representations and their corresponding tensor structures. These structures…

We collect evidence that the notion of path-ordered non-abelian integration admits an extension to two dimensions. We propose the corresponding notion of non-abelian 2-form along the lines of Lie algebroid theory and argue it is an…

Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…

We present the analytic computation of the master integrals associated to certain two-loop non-planar topologies, which are needed to complete the evaluation of the last two color coefficients for the top-pair production in the…

Real and virtual corrections in NNLO QCD require multi-dimensional integrals with overlapping singularities. We first review ideas and methods which have been proposed for performing such computations. We then present a new method for the…