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

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.

59 pages, final version

References in corpus (4)

• New Relations for Gauge-Theory Amplitudes
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• All tree-level amplitudes in massless QCD
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Cited by in corpus (14)

• Off-Shell Color-Kinematics Duality for Chern-Simons
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• New recursions for tree-level correlators in (Anti) de Sitter space
• One-loop off-shell amplitudes from classical equations of motion
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Color-kinematics duality from the Bern-Kosower formalism
• Manifest colour-kinematics duality and double-copy in the string-based formalism
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• Renormalisation in $\text{T}\bar{\text{T}}$-Deformed (Non-)Integrable Theories
• Next-to-MHV Yang-Mills kinematic algebra
• One-loop $N$-point correlators in pure gravity
• On the $L_{\infty }$ formulation of Chern-Simons theories
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras