A necessary ingredient for extending the BFKL equation to
next-to-next-to-leading logarithmic (NNLL) accuracy is the one-loop central
emission vertex (CEV) for two gluons which are not strongly ordered in
rapidity. Here we consider the one-loop six-gluon amplitude in N=4
super Yang-Mills (SYM) theory in a central next-to-multi-Regge kinematic (NMRK)
limit, we show that its dispersive part factorises in terms of the two-gluon
CEV, and we use it to extract the one-loop two-gluon CEV for any helicity
configuration within this theory. This is a component of the two-gluon CEV in
QCD. Although computed in the NMRK limit, both the colour structure and the
kinematic dependence of the two-gluon CEV capture much of the complexity of the
six-gluon amplitudes in general kinematics. In fact, the transcendental
functions of the latter can be conveniently written in terms of impact factors,
trajectories, single-emission CEVs and a remainder, which is a function of the
conformally invariant cross ratios which characterise the six-gluon amplitudes
in planar N=4 SYM. Finally, as expected, in the MRK limit the
two-gluon CEV neatly factorises in terms of two single-emission CEVs.Comment: 85 pages, 13 figure
