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arXiv · 1907.12154

$L_\infty$-algebras and the perturbiner expansion

Cristhiam Lopez-Arcos·Alexander Quintero Vélez
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Abstract

Certain classical field theories admit a formal multi-particle solution, known as the perturbiner expansion, that serves as a generating function for all the tree-level scattering amplitudes and the Berends-Giele recursion relations they satisfy. In this paper it is argued that the minimal model for the $L_{\infty}$-algebra that governs a classical field theory contains enough information to determine the perturbiner expansion associated to such theory. This gives a prescription for computing the tree-level scattering amplitudes by inserting the perturbiner solution into the homotopy Maurer-Cartan action for the $L_{\infty}$-algebra. We confirm the method in the non-trivial examples of bi-adjoint scalar and Yang-Mills theories.

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Cristhiam Lopez-Arcos, Alexander Quintero Vélez. 2019-07-28. $L_\infty$-algebras and the perturbiner expansion. https://doi.org/10.1007/jhep11(2019)010

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