Double copy for Lagrangians at trilinear order

TL;DR

This paper introduces a new double-copy method at the Lagrangian level that maps gauge theories to gravity, demonstrating equivalence at the trilinear order and deriving soft theorems for fermions.

Contribution

It presents a novel double-copy prescription for Lagrangians at trilinear order, connecting gauge theories to gravity and matter couplings.

Findings

Yang-Mills Lagrangian maps to supergravity in light-cone gauge

Equivalent to Einstein gravity at tree level up to trilinear order

Derivation of fermionic gravitational soft theorems

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.