Perturbiner Methods for Effective Field Theories and the Double Copy

Abstract

Perturbiner expansion provides a generating function for all Berends-Giele currents in a given quantum field theory. We apply this method to various effective field theories with and without color degrees of freedom. In the colored case, we study the U(N) non-linear sigma model of Goldstone bosons (NLSM) in a recent parametrization due to Cheung and Shen, as well as its extension involving a coupling to the bi-adjoint scalar. We propose a Lagrangian and a Cachazo-He-Yuan formula for the latter valid in multi-trace sectors and systematically calculate its amplitudes. Furthermore, we make a similar proposal for a higher-derivative correction to NLSM that agrees with the subleading order of the abelian Z-theory. In the colorless cases, we formulate perturbiner expansions for the special Galileon and Born-Infeld theories. Finally, we study Kawai-Lewellen-Tye-like double-copy relations for Berends-Giele currents between the above colored and colorless theories. We find that they hold up to pure gauge terms, but without the need for further field redefinitions.

44 pages

References in corpus (13)

• Black holes and the double copy
• The Momentum Kernel of Gauge and Gravity Theories
• Effective Field Theories from Soft Limits
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• New Identities among Gauge Theory Amplitudes
• Expansion of All Multitrace Tree Level EYM Amplitudes
• Unification of Galileon Dualities
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Note on New KLT relations

Cited by in corpus (46)

• Type D Spacetimes and the Weyl Double Copy
• Covariant Color-Kinematics Duality
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• On the Double Copy for Spinning Matter
• Classical double copy at null infinity
• On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators
• Tree-level amplitudes from the pure spinor superstring
• UV considerations on scattering amplitudes in a web of theories
• Soft Bootstrap and Effective Field Theories
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• $L_{\infty }$-algebras and the perturbiner expansion
• Radiation of scalar modes and the classical double copy
• New recursions for tree-level correlators in (Anti) de Sitter space
• Shift symmetries, soft limits, and the double copy beyond leading order
• Scattering Massive String Resonances through Field-Theory Methods
• Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
• The $L_{\infty }$ structure of gauge theories with matter
• One-loop off-shell amplitudes from classical equations of motion
• A Lie bracket for the momentum kernel
• Multiparticle solutions to Einstein's equations
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Color-kinematics duality from the Bern-Kosower formalism
• Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory
• The Infrared Structure of Exceptional Scalar Theories
• Higher-order tree-level amplitudes in the nonlinear sigma model
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• A Type of Unifying Relation in (A)dS Spacetime
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories
• New Factorization Relations for Non-Linear Sigma Model Amplitudes
• Renormalisation in $\text{T}\bar{\text{T}}$-Deformed (Non-)Integrable Theories
• Perturbations of General Relativity to All Orders and the General $n^{\mathrm{th}}$ Order Terms
• Berends-Giele currents for extended gravity
• Celestial Berends-Giele current
• Scattering Equations and Factorization of Amplitudes II: Effective Field Theories
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• One-loop $N$-point correlators in pure gravity
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
• The off-shell expansion relation of the Yang-Mills scalar theory
• Systematic approach to $\ell$-loop planar integrands from the classical equation of motion
• Quantum Off-Shell Recursion Relation
• The bi-adjoint scalar $\ell$-loop planar integrand recursion and graded inverse variables