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 → 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 → 3 and 2 → 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.Comment: 26 page