Theories of the gravity+gauge type in de Sitter space

TL;DR

The paper develops a covariant, connection- and curvature-based formulation of GR coupled to Yang-Mills in 4d with $\oldsymbol{\\Lambda}$, presenting real non-chiral and complex chiral Lagrangians that unify the two sectors in a double-copy–like structure. It then extends the framework to higher-spin self-dual GR+YM, proving gauge invariance and deriving a HS Lagrangian that preserves the full gauge symmetry, with a generating-function description of all spins. A lightcone gauge is constructed, yielding a cubic-exact action and an all-orders solution for HS self-dual YM; this framework is then descended to analyze lightcone gauges related by a shared lightray, relevant for de Sitter static-patch scattering. The paper demonstrates two complementary routes to relate lightcone gauges: a gauge-invariant field-strength approach and an explicit, though heuristic, gauge transformation, showing consistent mappings and opening pathways toward HS gravity and static-patch amplitudes in nonzero $\oldsymbol{\\Lambda}$. Overall, the work lays a robust foundation for off-shell double-copy structures, HS extensions, and de Sitter scattering within a covariant, gauge-symmetric formalism.

Abstract

We study theories of the "General Relativity + Yang-Mills" type in 4d spacetime with cosmological constant, focusing on formulations where the basic variables are connections and curvatures (but no metric). We present a new Lagrangian for GR coupled to Yang-Mills, which uses the same kind of variables for both sectors, and is suggestive of the double-copy structure. This Lagrangian comes in both non-chiral (real) and chiral (complex) versions. The chiral version makes it easy to isolate the self-dual sector. The latter lends itself to a higher-spin (HS) generalization, which combines the HS Self-Dual GR and HS Self-Dual Yang-Mills of Krasnov, Skvortsov and Tran. We then descend from the covariant formulation to lightcone gauge, and construct a cubic-exact lightcone action. For HS Self-Dual Yang-Mills, we solve the lightcone field equations to all orders in perturbation theory. Finally, we discuss the relation between lightcone foliations that share a lightray - a setup relevant for the scattering problem in the de Sitter static patch. We derive this relation at the linearized level, and argue from causality+symmetry that it cannot receive non-linear corrections. We explore the associated gauge transformations in the non-linear covariant theory.