Julian Lang

A bstract: We study Higher-Spin Gravity in 4-dimensional (Anti-)de Sitter space, at leading order in the interactions (cubic vertices), in the AdS lightcone formalism developed by Metsaev. Using the vertices’ chiral structure, we extend the formalism into a broader class of lightcone frames, which allows for lightcones of bulk points. This enables us to write the lightcone theory in de Sitter space, where only these more general frames are available. It also allows us to formulate and verify (for the first time!) some causal properties of massless higher-spin interactions, involving lightcone foliations that share a lightray. These causal properties serve to both motivate and enable the computation of “static-patch scattering amplitudes” — the evolution of fields between the two horizons of the maximal observable region in de Sitter space. We present a computation scheme for such “amplitudes” in coordinate space, and in momentum space with spinor-helicity variables.

A bstract: We develop a systematic approach to the computation of gauge invariant quartic interactions between reducible massive and massless higher spin fields. Extending the BRST formulation of existing cubic results, we obtain a single constraint for each off-shell quartic vertex that ensures both the gauge invariance of the Lagrangian and formal closure of the gauge algebra at quartic order. A solution to these equations is presented. The general equation is then reduced to an on-shell version to reduce complexity. We find example solutions for the off-shell and on-shell quartic vertices in low spin examples relevant to the problem of black hole scattering.

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.