Theories of the gravity+gauge type in de Sitter space

TL;DR

This paper develops a new connection-based Lagrangian for gravity coupled with Yang-Mills in de Sitter space, explores its chiral and higher-spin extensions, and analyzes lightcone gauge formulations and scattering implications.

Contribution

It introduces a novel, unified connection-based Lagrangian for GR and Yang-Mills with potential double-copy structure, and extends to higher-spin self-dual theories and lightcone analysis.

Findings

New connection-based Lagrangian for GR + Yang-Mills

Higher-spin self-dual generalizations constructed

Lightcone gauge action solved perturbatively

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.