This review describes the duality between color and kinematics and its applications, with the
aim of gaining a deeper understanding of the perturbative structure of gauge and gravity …

A bstract We compute classical gravitational observables for the scattering of two spinless
black holes in general relativity and\(\mathcal {N}\)= 8 supergravity in the formalism of …

Scattering amplitudes are both a wonderful playground to discover novel ideas in quantum
field theory and simultaneously of immense phenomenological importance to make …

Feynman diagrams constitute one of the essential ingredients for making precision
predictions for collider experiments. Yet, while the simplest Feynman diagrams can be …

A bstract We compute all master integrals for massless three-loop four-particle scattering
amplitudes required for processes like di-jet or di-photon production at the LHC. We present …

We define the rigidity of a Feynman integral to be the smallest dimension over which it is
nonpolylogarithmic. We prove that massless Feynman integrals in four dimensions have a …

A bstract We describe the minimal space of polylogarithmic functions that is required to
express the six-particle amplitude in planar\(\mathcal {N}\)= 4 super-Yang-Mills theory …

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 …

We present a compact analytic expression for the leading colour two-loop five-gluon
amplitude in Yang-Mills theory with a single negative helicity and four positive helicities. The …

A bstract The first paper of this series introduced objects (elements of twisted relative
cohomology) that are Poincaré dual to Feynman integrals. We show how to use the pairing …