Gauge invariant double copy of Yang-Mills theory: the quartic theory

Abstract

We give an explicit gauge invariant, off-shell and local double copy construction of gravity from Yang-Mills theory to quartic order. To this end we use the framework of homotopy algebras, and we identify a rich new algebraic structure associated to color-stripped Yang-Mills theory. This algebra, which is a generalization of a Batalin-Vilkovisky algebra, is the underlying structure necessary for double copy. We give a self-contained introduction into these algebras by illustrating them for Chern-Simons theory in three dimensions. We then construct N = 0 supergravity in the form of double field theory in terms of the algebraic Yang-Mills building blocks to quartic order in interactions. As applications of the same universal formula, we re-derive the 4-graviton scattering amplitude and compute a chiral form of the Courant algebroid gauge structure of double field theory.

arXiv comment30 pages plus appendix and references. Published version

References in corpus (40)

• New Relations for Gauge-Theory Amplitudes
• Double Field Theory
• Closed String Field Theory: Quantum Action and the BV Master Equation
• Introduction to string field theory
• Generalized metric formulation of double field theory
• Introduction to sh Lie algebras for physicists
• Superspace Duality in Low-Energy Superstrings
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Gravity as the Square of Gauge Theory
• Background independent action for double field theory
• Black holes and the double copy
• Double Field Theory: A Pedagogical Review
• The gauge algebra of double field theory and Courant brackets
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Radiation and the classical double copy for color charges
• The classical double copy for Taub-NUT spacetime
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Kerr Black Holes as Elementary Particles
• Perturbative spacetimes from Yang-Mills theory
• $L_{\infty }$ Algebras and Field Theory
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Gravitational Radiation from Color-Kinematics Duality
• Type D Spacetimes and the Weyl Double Copy
• Gravity Amplitudes as Generalized Double Copies
• Berends-Giele recursions and the BCJ duality in superspace and components
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• On factorizations in perturbative quantum gravity
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Classical Double Copy of Worldline Quantum Field Theory
• Double Field Theory as the Double Copy of Yang-Mills
• Conformal Field Theory and Algebraic Structure of Gauge Theory
• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
• BRST Symmetry and the Convolutional Double Copy

Cited by in corpus (8)

• Scattering Amplitudes in Quantum Field Theory
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Ambitwistor Yang-Mills Theory Revisited
• The Dark Side of Double-Tensor Multiplets