A simple collinear limit of scattering amplitudes at strong coupling

TL;DR

This work investigates a special collinear (multi-double-collinear) limit of strong-coupling scattering amplitudes in ${ m N}=4$ SYM, where all Y-system mass parameters $m_s$ are taken large. In this limit the free-energy $A_{free}$ vanishes and the periods part $A_{periods}$ is fixed by the relation $A_{periods}=-ig[(A_{BDS-like}-A_{BDS})+A_{extra}ig]$ evaluated at $m_s oty$, with careful treatment of phase-dependent cross ratios via the spectral parameter. The paper confirms known results for $n eq 4K$ up to eleven points and computes the periods part for eight- and twelve-point amplitudes for the first time, uncovering a monodromy-related correction $-rac{1}{4}|w_0|^2$ in the eight-point case and a corresponding structure for $n=12$. These results reinforce the consistency of the $Y$-system/HO Hirota framework for polygonal Wilson loops at strong coupling and sharpen the nonperturbative understanding of remainder functions in the AdS/CFT correspondence.

Abstract

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 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.