The L ∞ structure of gauge theories with matter
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Date
2021
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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∞-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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Keywords
BRST Quantization, Differential and Algebraic Geometry, Scattering Amplitudes
Citation
Gomez, H., Jusinskas, R. L., Lopez-Arcos, C., & Vélez, A. Q. (2021). The L ∞ structure of gauge theories with matter. Journal of High Energy Physics, 2021(2). https://doi.org/10.1007/JHEP02(2021)093