Gauge transformations in Z-space in (anti)holomorphic sector of HS theory

Abstract

We consider a consistent deformation of the (anti)holomorphic generating system of [arXiv:2209.01966], aiming to provide a map to the (anti)holomorphic truncation of the Vasiliev theory. In our new formulation, the previously rigidly defined master-field $Λ$ can be shifted by $\mathrm{d}_z$-exact projective one-forms. The class of projective one-forms is described comprehensively, and corresponding projective identities are proven. $\mathrm{d}_z$-exact forms of the order $n$ in $C$ induce field redefinition of order $(n+1)$ and beyond. Explicit expression for the $(n+1)$-th order field redefinitions are provided. An analysis of the gauge transformation of the second order in $C$ in zero-forms is performed, identifying necessary and sufficient conditions for the part of the field redefinition of the second order that can be gauged away. The field redefinitions induced by the shift of $Λ$ are proven to be nontrivial.