Manifestly dual-conformal loop integration

DOI10.1016/j.nuclphysb.2019.03.022zbMath1415.81040arXiv1901.02887OpenAlexW2911022111WikidataQ128098857 ScholiaQ128098857MaRDI QIDQ2423320

Erik Panzer, Falko Dulat, Jacob L. Bourjaily

Publication date: 21 June 2019

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.02887

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Yang-Mills and other gauge theories in quantum field theory (81T13) Feynman diagrams (81T18)

Related Items (18)

Building bases of loop integrands ⋮ Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space ⋮ RationalizeRoots: software package for the rationalization of square roots ⋮ Rooting out letters: octagonal symbol alphabets and algebraic number theory ⋮ Conformally-regulated direct integration of the two-loop heptagon remainder ⋮ Illustrations of integrand-basis building at two loops ⋮ Loop-by-loop differential equations for dual (elliptic) Feynman integrals ⋮ Cutting the traintracks: Cauchy, Schubert and Calabi-Yau ⋮ The stratification of rigidity ⋮ Spherical contours, IR divergences and the geometry of Feynman parameter integrands at one loop ⋮ All-mass \(n\)-gon integrals in \(n\) dimensions ⋮ Positive geometry, local triangulations, and the dual of the amplituhedron ⋮ Rationalizing loop integration ⋮ \textit{locally}-finite quantities in sYM ⋮ The Wilson-loop \(d\) log representation for Feynman integrals ⋮ Yangian Ward identities for fishnet four-point integrals ⋮ Direct Integration for Multi-Leg Amplitudes: Tips, Tricks, and When They Fail ⋮ The SAGEX review on scattering amplitudes Chapter 1: Modern fundamentals of amplitudes

Uses Software

• Hypexp
• CutTools
• BlackHat
• two loop amplitudes
• HyperInt
• positroids

Cites Work

• The four-loop remainder function and multi-Regge behavior at NNLLA in planar \( \mathcal{N} = 4\) super-Yang-Mills theory
• From the holomorphic Wilson loop to `d log' loop-integrands of super-Yang-Mills amplitudes.
• Eliminating spurious poles from gauge-theoretic amplitudes
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Scattering into the fifth dimension of \(\mathcal{N} = 4\) super Yang-Mills
• An analytic result for the two-loop hexagon Wilson loop in \( \mathcal{N} = 4 \) SYM
• Dual conformal symmetry of 1-loop NMHV amplitudes in \( \mathcal{N} = 4 \) SYM theory
• The Grassmannian origin of dual superconformal invariance
• A duality for the S matrix
• Higgs-regularized three-loop four-gluon amplitude in \( \mathcal{N} = 4 \) SYM: exponentiation and Regge limits
• Erratum to: ``Three-loop universal anomalous dimension of the Wilson operators in \(\mathcal N=4\) SUSY Yang-Mills model [Phys. Lett. B 595 (2004) 521]
• Simple loop integrals and amplitudes in \( \mathcal{N} = 4 \) SYM
• The Grassmannian and the twistor string: connecting all trees in \({\mathcal N} = 4\) SYM
• Local spacetime physics from the Grassmannian
• All tree-level amplitudes in massless QCD
• Unification of residues and Grassmannian dualities
• The all-loop integrand for scattering amplitudes in planar \({\mathcal N} = 4\) SYM
• Feynman integral evaluation by a sector decomposition approach (FIESTA)
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• Dual superconformal symmetry of scattering amplitudes in \({\mathcal N}=4\) super-Yang-Mills theory
• The no-triangle hypothesis for \(\mathcal N= 8\) supergravity
• Mellin transforms and asymptotics: Harmonic sums
• Prescriptive unitarity
• Analytic tools for Feynman integrals
• Hypexp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• Resolution of singularities for multi-loop integrals
• The box integrals in momentum-twistor geometry
• Hexagon functions and the three-loop remainder function
• Generalized unitarity and one-loop amplitudes in \(\mathcal N=1\) super-Yang-Mills
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• Numerical evaluation of multi-loop integrals by sector decomposition
• Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams
• Amplitudes and correlators to ten loops using simple, graphical bootstraps
• Feynman integrals and iterated integrals of modular forms
• Heptagons from the Steinmann cluster bootstrap
• Bootstrapping the QCD soft anomalous dimension
• Rationalizing loop integration
• Local integrals for planar scattering amplitudes
• One-loop \(n\)-point gauge theory amplitudes, unitarity and collinear limits.
• More loops and legs in Higgs-regulated \(\mathcal{N} = 4\) SYM amplitudes
• What is the simplest quantum field theory?
• Bootstrapping the three-loop hexagon
• Analytic result for the two-loop six-point NMHV amplitude in \(\mathcal{N} = {4}\) super Yang-Mills theory
• Six-gluon amplitudes in planar \(\mathcal{N} = 4\) super-Yang-Mills theory at six and seven loops
• Feynman integrals and iterated integrals on moduli spaces of curves of genus zero
• On-shell methods in perturbative QCD
• The double pentaladder integral to all orders
• Rationalizing roots: an algorithmic approach
• The two-loop hexagon Wilson loop in \(\mathcal{N}=4\) SYM
• Evaluating Feynman integrals.
• Elliptic multiple zeta values and one-loop superstring amplitudes
• Local integrand representations of all two-loop amplitudes in planar SYM
• Hedgehog bases for \(A_{n}\) cluster polylogarithms and an application to six-point amplitudes
• On the decomposition of motivic multiple zeta values
• New Representations of the Perturbative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:math>Matrix
• Amplitudes at weak coupling as polytopes in AdS₅
• Tree-level amplitudes and dual superconformal symmetry
• Relations between elliptic multiple zeta values and a special derivation algebra
• Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$
• HARMONIC POLYLOGARITHMS
• Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes
• A generalized scaling function for AdS/CFT
• An automatized algorithm to compute infrared divergent multi-loop integrals.
• The massless higher-loop two-point function
• Unnamed Item

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