标题： 分数自旋，展开和全息论：一。 对偶高自旋引力约简的母场方程 显示英文标题

标题： Fractional Spins, Unfolding, and Holography: I. Parent field equations for dual higher-spin gravity reductions

摘要： 在本工作中，以及在一篇配套论文中，我们基于AKSZ形式主义开启了全息理论的一种方法。 作为第一步，我们通过获得4D高自旋引力（HSG）和3D颜色共形高自旋引力（CCHSG）——即与共形高自旋规范场和颜色规范场耦合的颜色共形物质场——作为单一父理论的两个不同且经典一致的约化，从而改进了Vasiliev的全息理论提案，见arXiv:1203.5554。 后者在物理上由一个取值于Vasiliev高自旋代数的分数自旋扩展的平坦超连接组成。 4D HSG和3D CCHSG约化由对偶结构群和二形式上同调元素表征，它们在共同父模型中的嵌入为从圆柱体上的多维AKSZ配分函数导出全息关系提供了理由，这些关系将分别出现。 在本工作中，我们i) 构造了底层的非交换几何，作为一个在一对共形粒子的厄米模块中表示的元对称算子代数；ii) 识别了一个离散模群，该群来自第一量化系统的扭曲边界条件，并连接第二量化系统的不同边界条件；iii) 识别出表征HSG和CCHSG约化的绕行、结构群和二形式上同调元素，并将对偶的第二陈类相等。 显示英文摘要

摘要： In this work and in a companion paper we initiate an approach to holography based on the AKSZ formalism. As a first step, we refine Vasiliev's holography proposal in arXiv:1203.5554 by obtaining 4D higher-spin gravity (HSG) and 3D coloured conformal higher-spin gravity (CCHSG) -- i.e., coloured conformal matter fields coupled to conformal higher-spin gauge fields and colour gauge fields -- as two distinct and classically consistent reductions of a single parent theory. The latter consists, on-shell, of a flat superconnection valued in a fractional-spin extension of Vasiliev's higher-spin algebra. The 4D HSG and 3D CCHSG reductions are characterized by dual structure groups and two-form cohomology elements, and their embedding in a common parent model provides a rationale for deriving holographic relations from multi-dimensional AKSZ partition functions on cylinders with dual boundary conditions, to appear separately. In this work we i) construct the underlying non-commutative geometry as a metaplectic operator algebra represented in a Hermitian module of a pair of conformal particles; ii) identify a discrete modular group, arising from twisted boundary conditions of the first-quantized system, and connecting different boundary conditions of the second-quantized system; and iii) identify the holonomies, structure groups and two-form cohomology elements that characterize the HSG and CCHSG reductions, and equate the dual second Chern classes.