We consider a construction of observables by using methods of supersymmetric field theories. In particular, we give an extension of AKSZ-type observables constructed in Mnev (Lett Math Phys 105:1735–1783, 2015) using the Batalin–Vilkovisky structure of AKSZ theories to a formal global version with methods of formal geometry. We will consider the case where the AKSZ theory is “split” which will give an explicit construction for formal vector fields on base and fiber within the formal global action. Moreover, we consider the example of formal global generalized Wilson surface observables whose expectation values are invariants of higher-dimensional knots by using BF field theory. These constructions give rise to interesting global gauge conditions such as the differential quantum master equation and further extensions.

中文翻译：

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正式的全球AKSZ量具可观测值和广义Wilson曲面

我们考虑通过使用超对称场论的方法来构造可观察物。尤其是，我们将使用AKSZ理论的Batalin-Vilkovisky结构（使用形式几何方法）扩展到Mnev中构造的AKSZ型可观测物（Lett Math Phys 105：1735-1783，2015）。我们将考虑AKSZ理论是“分裂”的情况，这将为正式的全局动作中的基础和光纤上的形式矢量场提供明确的构造。此外，我们考虑使用BF的形式化全局广义Wilson曲面可观测值的示例，其期望值为高维结的不变量场论。这些构造引起了有趣的全局规范条件，例如微分量子主方程和进一步的扩展。