Minimal model of Chiral Higher Spin Gravity

Abstract

A unique class of local Higher Spin Gravities with propagating massless fields in 4d -Chiral Higher Spin Gravity -was first found in the light-cone gauge. We construct a covariant form of the corresponding field equations in all orders, thus completing the previous analysis of arxiv:2204.10285. This result is equivalent to taking the minimal model (in the sense of L ∞ -algebras) of the jet-space BV-BRST formulation of Chiral Higher Spin Gravity, thereby, containing also information about counterterms, anomalies, etc.

Chiral Higher Spin Gravity in (A)dS${}_4$ and secrets of Chern-Simons Matter Theories

“…Hereinafter we let ∆ n denote the n-dimensional simplex t 0 = 0 ≤ t 1 ≤ ... ≤ t n ≤ 1. This vertices deform smoothly those of Chiral Theory in flat space [33] and are simple λ-modifications of what can be extracted from [81].…”

“…Here we introduced the parameter λ associated with the cosmological constant. At λ = 0 we recover the free equations of Chiral Theory in flat space [32,33].…”

“…We refer the reader to [32,33] for a detailed discussion of the formalism as well as to the original papers [37,73] which correctly identify the free data and bits of interactions. The Chiral Theory can be defined as a unique Lorentz invariant and local completion of the free action 6…”

“…paper we construct a manifestly covariant form of equations of motion for Chiral Theory with cosmological constant. The equations are found in the form of a Free Differential Algebra by a smooth deformation of those proposed recently in [32,33]. This FDA can also be interpreted as the dual of an L ∞ -algebra.…”

“…A manifestly Lorentz-invariant formulation of Chiral Theory in flat space was found in [32,33] at the level of equations of motion. The equations were constructed in the form of a Free Differential Algebra [34][35][36], thereby, fulfilling the old ideas [37].…”