Double copy for Lagrangians at trilinear order

Abstract

We present a novel double-copy prescription for gauge fields at the Lagrangian level and apply it to the original double copy, couplings to matter and the soft theorem. The Yang-Mills Lagrangian in light-cone gauge is mapped directly to the $\mathcal{N}=0$ supergravity Lagrangian in light-cone gauge to trilinear order, and we show that the obtained result is manifestly equivalent to Einstein gravity at tree level up to this order. The application of the double-copy prescription to couplings to matter is exemplified by scalar and fermionic QCD and finally the soft-collinear effective QCD Lagrangian. The mapping of the latter yields an effective description of an energetic Dirac fermion coupled to the graviton, Kalb-Ramond, and dilaton fields, from which the fermionic gravitational soft and next-to-soft theorems follow.

v2: 31 pages, LaTeX, added Sec. 5 discussing scalar and fermion couplings, extended outlook and appendix. Matches published version

References in corpus (10)

• New Relations for Gauge-Theory Amplitudes
• Evidence for a New Soft Graviton Theorem
• The Kinematic Algebra From the Self-Dual Sector
• Soft sub-leading divergences in Yang-Mills amplitudes
• Taming Tree Amplitudes In General Relativity
• KLT relations from the Einstein-Hilbert Lagrangian
• Twofold Symmetries of the Pure Gravity Action
• The Double Copy Structure of Soft Gravitons
• On the Lagrangian formulation of the double copy to cubic order
• Color kinematic symmetric (BCJ) numerators in a light-like gauge

Cited by in corpus (6)

• Off-Shell Color-Kinematics Duality for Chern-Simons
• Double Field Theory as the Double Copy of Yang-Mills
• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
• Non-perturbative aspects of the self-dual double copy
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Gravitational soft theorem from emergent soft gauge symmetries