Unified Lagrangians for gravity and gauge theory

Abstract

We present a new Lagrangian formulation of General Relativity with cosmological constant, coupled to Yang-Mills gauge theory. The formulation has a manifest color/kinematics-dual structure, both in the choice of fundamental fields and in the way they appear in the Lagrangian. The color/kinematics duality is between gauge and Lorentz generators. The fundamental fields consists of 1-form connections and 0-form curvatures -- a structure inspired by higher-spin gravity. The new formulation can be arrived at by combining appropriate versions of the Plebanski and Chalmers-Siegel Lagrangians, and integrating out the Plebanski 2-form. The construction comes in chiral and non-chiral versions. The chiral version is slightly simpler, and highlights the self-dual sector. The non-chiral one makes parity manifest, and doesn't force us to complexify the theory.