Collinear and Regge behavior of 2 -> 4 MHV amplitude in N = 4 super Yang-Mills theory

TL;DR

This paper analyzes the collinear and Regge behavior of the 2-to-4 MHV amplitude in N=4 SYM by analytically continuing the AGMSV remainder function to the Mandelstam region and comparing with the BFKL predictions. It demonstrates that, in the double-logarithmic regime, the continuation reproduces the BFKL results up to five loops, with leading contributions stemming from the γ_1^−(p) piece of the anomalous dimension. The authors interpret these findings in Regge theory terms, arguing for a non-multiplicative renormalization in the collinear limit and the possible need for two-operator mixing to account for left/right singularities in the ω-plane. They also outline two candidate exponentiation schemes for the ω-dependent partial waves and emphasize that next-to-leading BFKL corrections are required to resolve remaining ambiguities. The work provides a detailed bridge between OPE-inspired collinear expansion and Regge-based BFKL dynamics in a highly nontrivial, multi-loop setting, with implications for the analytic structure of amplitudes in N=4 SYM.

Abstract

We investigate the collinear and Regge behavior of the 2 -> 4 MHV amplitude in N = 4super Yang-Mills theory in the BFKL approach. The expression for the remainder function in the collinear kinematics proposed by Alday, Gaiotto, Maldacena, Sever and Vieira is analytically continued to the Mandelstam region. The result of the continuation in the Regge kinematics shows an agreement with the BFKL approach up to to five-loop level. We present the Regge theory interpretation of the obtained results and discuss some issues related to a possible non-multiplicative renormalization of the remainder function in the collinear limit.

Figures (5)

• Figure 1: The $2 \to 4$ gluon scattering amplitude.
• Figure 2: The Mandelstam channel of the $2 \to 4$ gluon planar scattering amplitude.
• Figure 3: The paths $\mathbf{A}$ and $\mathbf{B}$ in the $u_3$-space. The phase $\psi$ is defined by $u_1=|u_1| e^{-i\psi}$ and takes values between $0$ and $2\pi$ in the course of the analytic continuation. The value of $u_3$ is the same at the initial and final points of the paths $\mathbf{A}$ and $\mathbf{B}$.
• Figure 4: The cut structure of $h_k(\sigma)$ and $h^{sub}_1(\sigma)$. The figure illustrates the paths $\mathbf{A}$ and $\mathbf{B}$ of the analytic continuation. $\sigma_0$ denotes some starting point of the analytic continuation. Both of the paths have the same starting and final points. The Regge kinematics corresponds to $\sigma_0 \to +\infty$.
• Figure 5: The paths $\mathbf{A}$ and $\mathbf{B}$ of the analytic continuation in the $\tilde{s}_2$-plane. The cross on the real axis denotes the initial point of the continuation. In the course of the analytic continuation along the path $\mathbf{B}$ we cross the branch cut on the real axis from $0$ to $-1$ and return to the initial point. For the path $\mathbf{A}$ we cross the cut from $-1$ to $-\infty$.