Vasiliev高自旋引力的亚辛表示和序（不）依赖性
Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
摘要：
我们研究了Vasiliev四维高自旋引力的算符形式，而没有提到一个特定的顺序。更确切地说，我们利用一对一的映射之间的运营商和符号的一个家庭的订购处方之间的插值和超越外尔和正常的排序。这种对应关系使我们能够微扰集成的Vasiliev系统在运营商的形式和各种规格。在非齐次辛群元素中扩展主域，并让乘积仅由群控制，我们指定了一族因子化规范，其中我们能够将系统积分到所有阶，产生精确解，包括但不限于以前文献中提出的精确解;然后，在第一阶，连接到一个家庭的旋转瓦西里耶夫规范，其中的解决方案可以表示在弗隆斯达尔领域。负责后一种变换的规范函数是明确地在一阶构造的。高斯符号的解析延拓促进了系统在各种排序中的分析，通过该解析延拓，人们可以区分和连接亚复盖的两个分支，并给出内部Klein算子作为定义解析δ密度的高斯δ序列的性质的基本原理。作为一个应用程序的一些技术在这里开发的，我们评估扭量空间威尔逊线观测我们的精确解，并显示其独立于辅助建设的几个第一subleading订单微扰理论。
英文摘要：
We investigate the formulation of Vasiliev's four-dimensional higher-spin gravity in operator form, without making reference to one specific ordering. More precisely, we make use of the one-to-one mapping between operators and symbols thereof for a family of ordering prescriptions that interpolate between and go beyond Weyl and normal orderings. This correspondence allows us to perturbatively integrate the Vasiliev system in operator form and in a variety of gauges. Expanding the master fields in inhomogenous symplectic group elements, and letting products be controlled only by the group, we specify a family of factorized gauges in which we are able to integrate the system to all orders, producing exact solutions, including but not restricted to ones presented previously in the literature; and then connect, at first order, to a family of rotated Vasiliev gauges in which the solutions can be represented in terms of Fronsdal fields. The gauge function responsible for the latter transformation is explicitly constructed at first order. The analysis of the system in various orderings is facilitated by an analytic continuation of Gaussian symbols, by means of which one can distinguish and connect the two branches of the metaplectic double cover and give a rationale to the properties of the inner Klein operators as Gaussian delta sequences defining analytic delta densities. As an application of some of the techniques here developed, we evaluate twistor space Wilson line observables on our exact solutions and show their independence from auxiliary constructs up to the few first subleading orders in perturbation theory.
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