Simple loop integrals and amplitudes in N=4 SYM

Abstract

We use momentum twistors to evaluate planar loop integrals. Infrared divergences are regulated by the recently proposed AdS-inspired mass regulator. We show that two-loop amplitudes in N=4 super Yang-Mills can be expanded in terms of basis integrals having twistor numerators. We argue that these integrals are considerably simpler compared to the ones conventionally used. Our case in point is the two-loop six-point MHV amplitude. We present analytical results for the remainder function in a kinematical limit, and find agreement with a recent Wilson loop computation. We also provide two-loop evidence that the logarithm of MHV amplitudes can be written in terms of simple twistor space integrals.

27 pages, 5 figures

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Cited by in corpus (45)

• Multiloop integrals in dimensional regularization made simple
• Local Integrals for Planar Scattering Amplitudes
• Lectures on differential equations for Feynman integrals
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• Notes on the scattering amplitude / Wilson loop duality
• Basics of Generalized Unitarity
• Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• The three-loop form factor in N=4 super Yang-Mills
• Generic multiloop methods and application to N=4 super-Yang-Mills
• New differential equations for on-shell loop integrals
• Bootstrapping pentagon functions
• Matter dependence of the four-loop cusp anomalous dimension
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• MHV Diagrams in Momentum Twistor Space
• Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
• Mellin Amplitudes for Dual Conformal Integrals
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• Landau Singularities and Symbology: One- and Two-loop MHV Amplitudes in SYM Theory
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• Dual conformal symmetry at loop level; massive regularization
• The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Manifestly Dual-Conformal Loop Integration
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Relations of loop partial amplitudes in gauge theory by Unitarity cut method
• Non-Chiral S-Matrix of N=4 Super Yang-Mills
• MHV Diagrams from an All-Line Recursion Relation
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Hidden Simplicity of Gauge Theory Amplitudes
• Higher loop mixed correlators in N=4 SYM
• Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion
• Some analytic results for two-loop scattering amplitudes
• Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
• Non-planar BCFW Grassmannian Geometries
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• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
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