The Two-Loop Symbol of all Multi-Regge Regions

Abstract

We study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N=4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximal functional transcendentality.

20 pages, v2: include details on functions f and g, make appendix consistent with main text, typesetting (published version)

References in corpus (15)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• An Operator Product Expansion for Polygonal null Wilson Loops
• Bootstrapping an NMHV amplitude through three loops
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• On the collinear limit of scattering amplitudes at strong coupling
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• Evaluating the 6-point Remainder Function Near the Collinear Limit
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Multi-Regge Limit of the n-Gluon Bubble Ansatz
• Heptagon Amplitude in the Multi-Regge Regime
• Strong Wilson polygons from the lodge of free and bound mesons

Cited by in corpus (13)

• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Cluster adjacency and the four-loop NMHV heptagon
• All-order amplitudes at any multiplicity in the multi-Regge limit
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• The Two-Loop Remainder Function for Eight and Nine Particles
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• All two-loop MHV remainder functions in multi-Regge kinematics
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• On a residual freedom of the next-to-leading BFKL eigenvalue in color adjoint representation in planar $\mathcal{N}=4$ SYM
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• Systematics of the Multi-Regge Three-Loop Symbol
• The Multi-Regge Limit from the Wilson Loop OPE
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills