We study theories of the “general relativity and Yang-Mills” type in four-dimensional spacetime with cosmological constant, focusing on formulations where the basic variables are connections and curvatures (but no metric). We present a new Lagrangian for general relativity (GR) coupled to Yang-Mills theory, which uses the same kinds of variables for both sectors and is suggestive of the double-copy structure. This Lagrangian comes in both nonchiral (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 theory of Krasnov et al. We then descend from the covariant formulation to the light cone gauge and construct a cubic-exact light cone action. For HS self-dual Yang-Mills theory, we solve the light cone field equations to all orders in perturbation theory. Finally, we discuss the relation between light cone foliations that share a light ray—a setup relevant for the scattering problem in the de Sitter space static patch. We derive this relation at the linearized level and argue from causality and symmetry that it cannot receive nonlinear corrections. We explore the associated gauge transformations in the nonlinear covariant theory.

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• Gauge theories
• General relativity formalism