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.

arXiv comment59 pages, final version

References in corpus (44)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Relations for Gauge-Theory Amplitudes
• Chern-Simons Theory with Vector Fermion Matter
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Antibracket, Antifields and Gauge-Theory Quantization
• Notes on Superconformal Chern-Simons-Matter Theories
• Recursion Relations for Gauge Theory Amplitudes with Massive Particles
• $L_{\infty }$ Algebras and Field Theory
• Non-factorizable Contributions to $B\to \pi \pi$ Decays
• Color-Kinematics Duality for QCD Amplitudes
• Double copy for massive quantum particles with spin
• Chern Simons duality with a fundamental boson and fermion
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• All tree-level amplitudes in massless QCD
• On amplitudes in self-dual sector of Yang-Mills theory
• Berends-Giele recursions and the BCJ duality in superspace and components
• Berends-Giele recursion for double-color-ordered amplitudes
• Noncommutative homotopy algebras associated with open strings
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• All-Multiplicity Amplitudes with Massive Scalars
• Perturbiner Methods for Effective Field Theories and the Double Copy
• Helicity amplitudes for QCD with massive quarks
• Four Lectures on Closed String Field Theory
• Scattering Amplitude Recursion Relations in BV Quantisable Theories
• The Double Copy of Massive Scalar-QCD
• A solution to the non-linear equations of D=10 super Yang-Mills theory
• SD Perturbiner in YM+Gravity
• Algorithmic construction of SYM multiparticle superfields in the BCJ gauge
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• $L_{\infty }$-algebras and the perturbiner expansion
• Loop Amplitudes and Quantum Homotopy Algebras
• On tree form-factors in (supersymmetric) Yang-Mills theory
• Dressed scalar propagator in a non-abelian background from the worldline formalism
• Getting more flavour out of one-flavour QCD
• All tree level scattering amplitudes in Chern-Simons theories with fundamental matter
• Gravitationally dressed Parke-Taylor amplitudes
• $L_{\infty }$-Algebras, the BV Formalism, and Classical Fields
• Proof of a new colour decomposition for QCD amplitudes
• SFT-inspired Algebraic Structures in Gauge Theories
• Matter Chern Simons Theories in a Background Magnetic Field
• New relations for graviton-matter amplitudes
• Gravitational SD Perturbiner
• On form-factors in Sin(h)-Gordon theory

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