Discontinuites of BFKL amplitudes and the BDS ansatz

TL;DR

This paper investigates the discontinuities of multi-gluon production amplitudes within the BFKL framework and finds contradictions with the BDS ansatz in N=4 supersymmetric Yang-Mills theory, providing explicit formulas for certain cases.

Contribution

It presents explicit expressions for discontinuities of 2→3 and 2→4 amplitudes in N=4 SYM and highlights contradictions with the BDS ansatz, advancing understanding of amplitude structures.

Findings

Discontinuities of 2→2 + n amplitudes contradict the BDS ansatz.

Explicit formulas for 2→3 and 2→4 amplitude discontinuities are derived.

Results can test the duality between Wilson loops and MHV amplitudes.

Abstract

We perform an examination of discontinuities of multiple production amplitudes, which are required for further development of the BFKL approach. It turns out that the discontinuities of 2 $\to$ 2 + n amplitudes obtained in the BFKL approach contradict to the BDS ansatz for amplitudes with maximal helicity violation in N = 4 supersymmetric Yang-Mills theory with large number of colours starting with n = 2. Explicit expressions for the discontinuities of the 2 $\to$ 3 and 2 $\to$ 4 amplitudes in the invariant mass of pairs of produced gluons are obtained in the planar N=4 SYM in the next-to-leading logarithmic approximation. These expressions can be used for checking the conjectured duality between the light-like Wilson loops and the MHV amplitudes.