Yasha Neiman

We consider cubic interactions of massless fields of arbitrary spin in four spacetime dimensions, within the light cone formalism. We extend two key results from flat to (anti-)de Sitter spacetime. First, we present a simple explicit expression for all the cubic vertices. Second, we prove that the various self-dual/chiral theories, such as self-dual Yang-Mills, self-dual general relativity, and chiral higher-spin gravity, are fully consistent with no need for vertices beyond cubic. The key observation behind our results is that all cubic vertices in the light cone formalism can be expressed as a direct generalization of the “Abelian” vertices formed by multiplying linearized curvatures. The simple relationship between flat and (anti-)de Sitter then follows essentially from the conformal invariance of such linearized curvatures. The price for such simplicity is that our vertex expressions are nonlocal. It is, however, easy to bring them into a local form, which we also present.

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.

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.

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.

In this paper we study topology-changing spacetimes occurring from pointlike sources. Following an old idea of Penrose, we will opt for a non-Hausdorff model of topology change in which an initial pointlike source is “doubled” and allowed to propagate along null rays into an eventual cobordism. By appealing to recent developments in non-Hausdorff differential geometry, we will describe and evaluate gravitational actions on these topology-changing spacetimes. Motivated by analogous results for the Trousers space, we describe a sign convention for Lorentzian angles that will ensure the dampening of our non-Hausdorff topology-changing spacetimes within a two-dimensional path integral for gravity.

We study the higher-spin extension of self-dual General Relativity (GR) with cosmological constant, proposed by Krasnov, Skvortsov and Tran. We show that this theory is actually a gauge-fixing of a 6d diffeomorphism-invariant Abelian theory, living on (4d spacetime)×(2d spinor space) modulo a finite group. On the other hand, we point out that the theory respects the 4d geometry of a self-dual GR solution, with no backreaction from the higher-spin fields. We also present a lightcone ansatz that reduces the covariant fields to one scalar field for each helicity. The field equations governing these scalars have only cubic vertices. We compare our lightcone ansatz to Metsaev’s lightcone formalism. We conclude with a new perspective on the lightcone formalism in (A)dS spacetime: not merely a complication of its Minkowski-space cousin, it has a built-in Lorentz covariance, and is closely related to Vasiliev’s concept of unfolding.

We study the higher-spin extension of self-dual General Relativity (GR) with cosmological constant, proposed by Krasnov, Skvortsov and Tran. We show that this theory is actually a gauge-fixing of a 6d diffeomorphism-invariant Abelian theory, living on (4d spacetime)x(2d spinor space) modulo a finite group. On the other hand, we point out that the theory respects the 4d geometry of a self-dual GR solution, with no backreaction from the higher-spin fields. We also present a lightcone ansatz that reduces the covariant fields to one scalar field for each helicity. The field equations governing these scalars have only cubic vertices. We compare our lightcone ansatz to Metsaev's lightcone formalism. We conclude with a new perspective on the lightcone formalism in (A)dS spacetime: not merely a complication of its Minkowski-space cousin, it has a built-in Lorentz covariance, and is closely related to Vasiliev's concept of unfolding.

Using Krasnov's formulation of General Relativity (GR), we develop a lightcone ansatz for self-dual gravity (along with linearized anti-self-dual perturbations) in the Poincare patch of de Sitter space. This amounts to a generalization of Plebanski's "second heavenly equation" to non-zero cosmological constant. The only interaction vertices are cubic ones, found previously by Metsaev in a bottom-up lightcone approach. We point out a special feature of these vertices, which leads to "almost conservation" of energy at each successive order in perturbation theory, despite the time-dependent de Sitter background. Since we embed the lightcone variables into a full spacetime metric, the solutions have a clear geometric interpretation. In particular, this allows us to read off boundary data on both the past and future horizons of a causal (static) patch. In this way, we add self-dual GR to the program of defining & computing scattering amplitudes in a causal patch of de Sitter space.

Using Krasnov’s formulation of general relativity, we develop a light cone ansatz for self-dual gravity (along with linearized anti-self-dual perturbations) in the Poincare patch of de Sitter space. This amounts to a generalization of Plebanski’s “first heavenly equation” to nonzero cosmological constant. The only interaction vertices are cubic ones, found previously by Metsaev in a bottom-up light cone approach. We point out a special feature of these vertices, which leads to “almost conservation” of energy at each successive order in perturbation theory, despite the time-dependent de Sitter background. Since we embed the light cone variables into a full spacetime metric, the solutions have a clear geometric interpretation. In particular, this allows us to read off boundary data on both the past and future horizons of a causal (static) patch. In this way, we add self-dual general relativity to the program of defining and computing scattering amplitudes in a causal patch of de Sitter space.