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arXiv · 2412.16106

Full S-matrices and Witten diagrams with (relative) L-infinity algebras

Luigi Alfonsi·Leron Borsten·Hyungrok Kim·Martin Wolf·Charles Alastair Stephen Young
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Abstract

The $L_\infty$-algebra approach to scattering amplitudes elegantly describes the nontrivial part of the $S$-matrix but fails to take into account the trivial part. We argue that the trivial contribution to the $S$-matrix should be accounted for by another, complementary $L_\infty$-algebra, such that a perturbative field theory is described by a cyclic relative $L_\infty$-algebra. We further demonstrate that this construction reproduces Witten diagrams that arise in AdS/CFT including, in particular, the trivial Witten diagrams corresponding to CFT two-point functions. We also discuss Chern-Simons theory and Yang-Mills theory on manifolds with boundaries using this approach.

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Luigi Alfonsi, Leron Borsten, Hyungrok Kim, Martin Wolf, Charles Alastair Stephen Young. 2024-12-20. Full S-matrices and Witten diagrams with (relative) L-infinity algebras. https://doi.org/10.1007/jhep07(2025)267

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