AI 中文总结
本文研究HS理论（反）全纯扇区的规范变换，通过形变生成系统建立与Vasiliev理论（反）全纯截断的映射，给出高阶场重定义及规范变换相关条件，证明其非平凡性。
AI 中文摘要
我们考虑对arXiv:2209.01966中（反）全纯生成系统的一致形变，旨在建立通往Vasiliev理论（反）全纯截断的映射。在新表述中，此前刚性定义的主场Λ可被dz-恰当的射影1-形式移位。本文全面描述了射影1-形式的类别，并证明了对应的射影恒等式。C中n阶的dz-恰当形式会诱导出n阶及以上的场重定义，文中给出了n+1阶场重定义的显式表达式。我们对零形式中C的二阶规范变换展开分析，确定了可被规范消除的二阶场重定义部分的充要条件，同时证明了由Λ的移位诱导的场重定义是非平凡的。
英文摘要
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.
