In planar N=4 SYM the IR-finite hard amplitude satisfies an uncorrected tree-level soft theorem and represents the undeformed tree-level S-algebra of soft gluons.
Magnea,Non-abelian infrared divergences on the celestial sphere,JHEP05(2021) 282, [arXiv:2104.10254]
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Loop-level Carrollian amplitudes in N=4 SYM and N=8 supergravity are differential operators on tree-level versions, with logarithmic eikonal behavior and IR-safe factorization via natural splitting.
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Soft Algebra for ${\cal N}=4$ SYM
In planar N=4 SYM the IR-finite hard amplitude satisfies an uncorrected tree-level soft theorem and represents the undeformed tree-level S-algebra of soft gluons.
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On Carrollian Loop Amplitudes for Gauge Theory and Gravity
Loop-level Carrollian amplitudes in N=4 SYM and N=8 supergravity are differential operators on tree-level versions, with logarithmic eikonal behavior and IR-safe factorization via natural splitting.
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