A simple collinear limit of scattering amplitudes at strong coupling

Collinear limit usually provides strong constraints for scattering amplitudes. At strong coupling, collinear limit of the amplitudes in N=4 SYM is related to the large mass limit of the corresponding Y system. In this paper, we consider a special case in which all mass parameters are taken to be large, which corresponds to a multi-double-collinear limit in which a n-side polygon becomes pentagons. This limit provides a useful constraint for the amplitudes, in particular can be used to fix the periods part for the case of 4K gluons, which is the last missing piece of full amplitudes.