Disentanglement of Topological and Dynamical Fields in 3d Higher-Spin Theory within Shifted Homotopy Approach

TL;DR

This paper derives the first-order corrections in 3d higher-spin theory using shifted homotopy, identifying a new cohomology class that separates dynamical and topological fields, and relates to mass deformation.

Contribution

It introduces a shifted homotopy method to disentangle dynamical and topological fields in 3d higher-spin theory, revealing a new cohomology class distinct from previous solutions.

Findings

Disentangled equations for dynamical and topological fields.

Identified a new cohomology class related to mass deformation.

Showed the solution differs from earlier direct method solutions.

Abstract

The first-order correction to the one-form sector of equations of the $3d$ higher-spin theory is derived from the generating nonlinear HS system by virtue of the shifted homotopy approach. The family of solutions to the generating system that disentangles equations for dynamical and topological fields in the first order of perturbation theory is found. This family is shown to belong to the different cohomology class compared to the solution found earlier by the direct methods. The related cohomology is shown to be the same as that underlying the mass deformation in the matter sector of $3d$ higher-spin equations.