More loops and legs in Higgs-regulated N=4 SYM amplitudes

Abstract

We extend the analysis of Higgs-regulated planar amplitudes of N=4 supersymmetric Yang-Mills theory to four loops for the four-gluon amplitude and to two loops for the five-gluon amplitude. Our calculations are consistent with a proposed all-loop ansatz for planar MHV n-gluon amplitudes that is the analog of the BDS ansatz in dimensional regularization. In all cases considered, we have verified that the IR-finite parts of the logarithm of the amplitudes have the same dependence on kinematic variables as the corresponding functions in dimensionally-regulated amplitudes (up to overall additive constants, which we determine). We also study various Regge limits of N=4 SYM planar n-gluon amplitudes. Euclidean Regge limits of Higgs-regulated n \geq 4 amplitudes yield results similar in form to those found using dimensional regularization, but with different expressions for the gluon trajectory and Regge vertices resulting from the different regulator scheme. We also show that the Regge limit of the four-gluon amplitude is dominated at next-to-leading-log order by vertical ladder diagrams together with the class of vertical ladder diagrams with a single H-shaped insertion.

34 pages, 5 figures; v2: references added; v3: minor changes, published version

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Cited by in corpus (49)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• From polygons and symbols to polylogarithmic functions
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Notes on the scattering amplitude / Wilson loop duality
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• The cusp anomalous dimension at three loops and beyond
• Generalized Unitarity and Six-Dimensional Helicity
• 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
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• Massive amplitudes on the Coulomb branch of N=4 SYM
• The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals
• Wilson line approach to gravity in the high energy limit
• Simple loop integrals and amplitudes in N=4 SYM
• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual conformal symmetry at loop level; massive regularization
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension
• Loop-level gluon OPEs in celestial holography
• Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes
• Manifestly Dual-Conformal Loop Integration
• Subleading Regge limit from a soft anomalous dimension
• Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• Amplitudes for massive vector and scalar bosons in spontaneously-broken gauge theory from the CHY representation
• Hidden Simplicity of Gauge Theory Amplitudes
• Integrands for QCD rational terms and N=4 SYM from massive CSW rules
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• The Coulomb-branch S-matrix from massless amplitudes
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Yangian Symmetry in N=4 super Yang-Mills
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• One-Loop N = 4 Super Yang-Mills Scattering Amplitudes to All Orders in the Dimensional Regularization Parameter
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• All-loop-orders relation between Regge limits of $\mathcal{N}=4$ SYM and $\mathcal{N}=8$ supergravity four-point amplitudes
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• BCFW Deformation and Regge Limit
• Yangian symmetry of light-like Wilson loops
• Two-loop D-dimensional unitarity and dual conformal symmetry
• A note on scattering amplitudes on the moduli space of ABJM