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.
Highlights
JHEP05(2016)012 multi-Regge kinematics is based on elementary building blocks, such as BFKL eigenvalues, impact factors and production vertices
We study the symbol of the two-loop n-gluon Maximally Helicity Violating (MHV) amplitude for all Mandelstam regions in multi-Regge kinematics in N = 4 super Yang-Mills theory
We complete the construction through a prescription for how to build the two-loop symbol in the multi-Regge limit of 2n−4 Mandelstam regions for any number of external gluons from the building blocks f and g
Summary
Let us consider the (3n − 15)-dimensional space X of independent dual conformal invariant cross ratios for an n-gluon scattering process, and a curve γ : [0, 1] → X in the space of kinematic invariants. Note that the symbol forgets all information encoded in the choice of the base point and path It determines the original iterated integral R only up to certain functions of lower transcendentality. Commutators of elements in the homotopy group are related to double discontinuities, and these are expressed through iterated integrals of transcendentality at most two. Such integrals do not show up in a symbol of length three and we will be able to safely ignore the difference between homotopy and homology in the following analysis
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