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arXiv · 2011.09528

The $L_{\infty}$ structure of gauge theories with matter

Humberto Gomez·Renann Lipinski Jusinskas·Cristhiam Lopez-Arcos·Alexander Quintero Velez
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Abstract

In this work we present an algebraic approach to the dynamics and perturbation theory at tree-level for gauge theories coupled to matter. The field theories we will consider are: Chern-Simons-Matter, Quantum Chromodynamics, and scalar Quantum Chromodynamics. Starting with the construction of the master action in the classical Batalin-Vilkovisky formalism, we will extract the $L_{\infty}$-algebra that allow us to recursively calculate the perturbiner expansion from its minimal model. The Maurer-Cartan action obtained in this procedure will then motivate a generating function for all the tree-level scattering amplitudes. There are two interesting outcomes of this construction: a generator for fully-flavoured amplitudes via a localisation on Dyck words; and closed expressions for fermion and scalar lines attached to $n$-gluons with arbitrary polarisations.

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Humberto Gomez, Renann Lipinski Jusinskas, Cristhiam Lopez-Arcos, Alexander Quintero Velez. 2021-02-11. The $L_{\infty}$ structure of gauge theories with matter. https://doi.org/10.1007/jhep02(2021)093

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