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arXiv · 2606.08582

Soft Algebra for ${\cal N}=4$ SYM

Luis F. Alday·Andrew Strominger
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Abstract

Scattering amplitudes of $n$ particles in nonabelian gauge theories admit factorizations of the general form $\mathcal{A}_n \;=\; \mathcal{A}^{\rm soft}_n \times \mathcal{A}^{\rm hard}_n$, where $\mathcal{A}^{\rm soft}_n$ is IR divergent, while $\mathcal{A}^{\rm hard}_n$ is IR finite and encodes the higher loop corrections to scattering. We specify a particular all-orders definition of this factorization for planar ${\cal N}=4$ super Yang-Mills (SYM) and argue that the resulting $\mathcal{A}_n^{\rm hard}$ obeys an uncorrected tree-level soft theorem. Moreover it furnishes a representation of the undeformed tree-level $\cal S$-algebra generated by a tower of soft gluons. The results follow from several commonly invoked assumptions for ${\cal N}=4$ SYM, including BDS one-loop exponentiation of the splitting function and amplitude/Wilson-loop duality.

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Luis F. Alday, Andrew Strominger. 2026-06-07. Soft Algebra for ${\cal N}=4$ SYM. https://arxiv.org/abs/2606.08582

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