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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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.
Bulk double soft limits introduce subtleties absent from boundary celestial CFTs, so the full soft expansion of gravitational amplitudes cannot be generated from the first three terms via celestial algebras.
citing papers explorer
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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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Soft Algebras via Bulk Double Soft Limits
Bulk double soft limits introduce subtleties absent from boundary celestial CFTs, so the full soft expansion of gravitational amplitudes cannot be generated from the first three terms via celestial algebras.