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Article
Open AccessOne-loop integrals from volumes of orthoschemes
Recently in ar**v:2012.05599 Rudenko presented a formula for the volume of hyperbolic orthoschemes in terms of alternating polylogarithms. We use this result to provide an explicit analytic result for the one-...
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Article
Open AccessConstraints on sequential discontinuities from the geometry of on-shell spaces
We present several classes of constraints on the discontinuities of Feynman integrals that go beyond the Steinmann relations. These constraints follow from a geometric formulation of the Landau equations that ...
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Article
Open AccessCuts and isogenies
We consider the genus-one curves which arise in the cuts of the sunrise and in the elliptic double-box Feynman integrals. We compute and compare invariants of these curves in a number of ways, including Feynma...
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Article
Open AccessSequential discontinuities of Feynman integrals and the monodromy group
We generalize the relation between discontinuities of scattering amplitudes and cut diagrams to cover sequential discontinuities (discontinuities of discontinuities) in arbitrary momentum channels. The new rel...
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Chapter
Direct Integration for Multi-Leg Amplitudes: Tips, Tricks, and When They Fail
Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a variety of results by the authors...
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Article
Open AccessAll-mass n-gon integrals in n dimensions
We explore the correspondence between one-loop Feynman integrals and (hyperbolic) simplicial geometry to describe the all-mass case: integrals with generic external and internal masses. Specifically, we focus on
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Article
Open AccessTraintrack Calabi-Yaus from twistor geometry
We describe the geometry of the leading singularity locus of the traintrack integral family directly in momentum twistor space. For the two-loop case, known as the elliptic double box, the leading singularity ...
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Article
Open AccessRooting out letters: octagonal symbol alphabets and algebraic number theory
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 s...
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Article
Open AccessEmbedding Feynman integral (Calabi-Yau) geometries in weighted projective space
It has recently been demonstrated that Feynman integrals relevant to a wide range of perturbative quantum field theories involve periods of Calabi-Yau manifolds of arbitrarily large dimension. While the number...
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Chapter and Conference Paper
Polylogarithm Identities, Cluster Algebras and the \(\mathcal {N} = 4\) Supersymmetric Theory
Scattering amplitudes in \(\mathcal {N} = 4\) super-Yang Mills theory can be computed to higher perturbative orders than in any other four-dimensional quantum field theory. The results are interesting transcenden...
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Article
Open AccessSmooth Wilson loops in \( \mathcal{N}=4 \) non-chiral superspace
We consider a supersymmetric Wilson loop operator for 4d N = 4 super Yang-Mills theory which is the natural object dual to the AdS 5 × S ...
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Article
Open AccessIntegrability of smooth Wilson loops in \( \mathcal{N}=4 \) superspace
We perform a detailed study of the Yangian symmetry of smooth supersymmetric Maldacena-Wilson loops in planar ...
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Article
Twistors, harmonics and holomorphic Chern-Simons
We show that the off-shell \( \mathcal{N}=3 \) action of \( \mathcal{N}=4 \) super Yang-Mills can be written as a holomorphic Chern-Simons actio...
