Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory

Abstract

In this paper we give all the details of the calculation that we presented in our previous paper ArXiv:0908.0387 where the infrared structure of the MHV gluon amplitudes in the planar limit for $\mathcal{N}=4$ super Yang-Mills theory was considered in the next-to-leading order of perturbation theory. Explicit cancellation of the infrared divergencies in properly defined inclusive cross-sections is demonstrated first in a toy model example of "conformal QED" and then in the real $\mathcal{N}=4$ SYM theory. We give the full-length details both for the calculation of the real emission and for the diagrams with splitting in initial and final states. The finite parts for some inclusive differential cross-sections are presented in an analytical form. In general, contrary to the virtual corrections, they do not reveal any simple structure. An example of the finite part containing just the log functions is presented. The dependence of inclusive cross-section on the external scale related to the definition of asymptotic states is discussed.

49 pages, LATEX, 6 eps figures; Minor changes, Refs added

References in corpus (25)

• Gluon scattering amplitudes at strong coupling
• Conformal collider physics: Energy and charge correlations
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• On the highest transcendentality in N=4 SUSY
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Exacting N=4 Superconformal Symmetry
• Four-Loop Cusp Anomalous Dimension From Obstructions
• On T-Duality and Integrability for Strings on AdS Backgrounds
• Strong-coupling expansion of cusp anomaly from quantum superstring
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Symmetries of the N=4 SYM S-matrix
• Infrared Safe Observables in $\mathcal{N}=4$ Super Yang-Mills Theory
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• One-loop derivation of the Wilson polygon - MHV amplitude duality

Cited by in corpus (8)

• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• On form factors in N=4 sym
• On the renormalization of multiparton webs
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• Dijet Production at Large Rapidity Separation in N=4 SYM
• On NMHV form factors in N=4 SYM theory from generalized unitarity
• On DIS Wilson coefficients in N = 4 super Yang-Mills theory
• Infrared Finite Observables in N=8 Supergravity