Type-B Formal Higher Spin Gravity

TL;DR

This paper develops non-linear equations for Type-B Higher Spin Gravity, connecting it to free fermion and Gross-Neveu models, derived from fundamental principles ensuring gauge invariance of the boundary CFT.

Contribution

It introduces a novel set of non-linear equations for Type-B Higher Spin Gravity directly derived from gauge invariance principles, applicable to various boundary conditions.

Findings

Derived equations describe propagation of mixed-symmetry fields

Equations are consistent with dual free fermion and Gross-Neveu models

Framework is based on gauge invariance of the CFT partition function

Abstract

We propose non-linear equations for the formal Type-B Higher Spin Gravity that is dual to the free fermion or to the Gross-Neveu model, depending on the boundary conditions. The equations are directly obtained from the first principles: the gauge invariance of the CFT partition function on an arbitrary background for single-trace operators. We also get equations describing propagation of certain mixed-symmetry fields over higher spin flat backgrounds.