Minimal models of field theories: Chiral Higher Spin Gravity

TL;DR

This paper develops a covariant formulation of Chiral Higher Spin Gravity in four dimensions, extending it to include related theories and providing a mathematical framework using $L_$-algebras and jet-space extensions.

Contribution

It constructs a covariant form of Chiral Higher Spin Gravity as a Free Differential Algebra up to NLO, incorporating related theories and a minimal model via $L_$-algebras.

Findings

Covariant formulation of Chiral Higher Spin Gravity achieved.

Includes covariant forms of higher spin extensions of SDYM and SDGR.

Mathematical framework using minimal models and jet-space extensions established.

Abstract

There exists a unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity. Originally, it was formulated in the light-cone gauge. We construct a covariant form of this theory as a Free Differential Algebra up to NLO, i.e. at the level of equations of motion. It also contains the recently discovered covariant forms of the higher spin extensions of SDYM and SDGR, as well as SDYM and SDGR themselves. From the mathematical viewpoint the result is equivalent to taking the minimal model (in the sense of $L_\infty$-algebras) of the jet-space extension of the BV-BRST formulation of Chiral Higher Spin Gravity, thereby, containing also information about (presymplectic AKSZ) action, counterterms, anomalies, etc.