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

High Energy Physics - Theory 2022-08-05 v2 Mathematical Physics Algebraic Geometry math.MP Representation Theory

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 LL_{\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 nn-gluons with arbitrary polarisations.

Keywords

Cite

@article{arxiv.2011.09528,
  title  = {The $L_{\infty}$ structure of gauge theories with matter},
  author = {Humberto Gomez and Renann Lipinski Jusinskas and Cristhiam Lopez-Arcos and Alexander Quintero Velez},
  journal= {arXiv preprint arXiv:2011.09528},
  year   = {2022}
}

Comments

59 pages, final version