Higher-spin self-dual General Relativity: 6d and 4d pictures, covariant vs. lightcone

TL;DR

This paper explores a higher-spin extension of self-dual General Relativity, revealing its gauge structure in 6d, its geometric properties in 4d, and presenting a covariant lightcone approach with simplified scalar field equations.

Contribution

It demonstrates that the higher-spin self-dual GR is a gauge-fixed form of a 6d diffeomorphism-invariant Abelian theory and introduces a covariant lightcone formalism with scalar fields for each helicity.

Findings

The theory is a gauge-fixing of a 6d Abelian theory.

The 4d geometry of self-dual GR is preserved without backreaction.

The lightcone ansatz reduces fields to scalar fields with cubic interactions.

Abstract

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.