The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory

TL;DR

This work investigates the multi-Regge limit of NMHV amplitudes in planar $\mathcal{N}=4$ SYM by comparing the BFKL formalism in leading logarithmic approximation with superconformal amplitude computations. It demonstrates exact agreement with two-loop results for six-point $2\to 4$ and $3\to 3$ processes and furnishes predictions for three-loop NMHV and certain $N^kMHV$ cases using the BFKL framework, expressed through the NMHV ratio function $\mathcal{P}_{NMHV}$ in terms of the cross-ratio variables and the complex momentum variable $w$. The analysis includes the real parts via dispersion relations, clarifies the role of Mandelstam cuts and the collinear limit, and extends to more legs (e.g., $2\to 5$) with analogous structure, exposing a coherent picture across MRK, BFKL, and OPE perspectives. The results solidify the consistency between different methods in the MRK regime and provide concrete higher-loop predictions to guide future calculations and cross-checks with OPE-based approaches.

Abstract

We consider the multi-Regge limit for N=4 SYM NMHV leading color amplitudes in two different formulations: the BFKL formalism for multi-Regge amplitudes in leading logarithm approximation, and superconformal N=4 SYM amplitudes. It is shown that the two approaches agree to two-loops for the 2->4 and 3->3 six-point amplitudes. Predictions are made for the multi-Regge limit of three loop 2->4 and 3->3 NMHV amplitudes, as well as a particular sub-set of two loop 2 ->2 +n N^kMHV amplitudes in the multi-Regge limit in the leading logarithm approximation from the BFKL point of view.

Figures (3)

• Figure 1: The $2 \to 4$ scattering amplitude in Euclidean region.
• Figure 2: Mandelstam region for $2 \to 4$ amplitude.
• Figure 3: One of the Mandelstam regions for $2 \to 5$ amplitude in which the remainder function reduces to the $2 \to 4$ case with redefined momenta.