We construct a formal global quantization of the Poisson Sigma Model in the BV-BFV formalism using the perturbative quantization of AKSZ theories on manifolds with boundary and analyze the properties of the boundary BFV operator. Moreover, we consider mixed boundary conditions and show that they lead to quantum anomalies, i.e. to a failure of the (modified differential) Quantum Master Equation. We show that it can be restored by adding boundary terms to the action, at the price of introducing corner terms in the boundary operator. We also show that the quantum Grothendieck BFV operator on the total space of states is a differential, i.e. squares to zero, which is necessary for a well-defined BV cohomology.

中文翻译：

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论BV-BFV形式主义中泊松西格玛模型的全球化

我们使用 AKSZ 理论的微扰量化在有边界的流形上构建了 BV-BFV 形式主义中泊松西格玛模型的正式全局量化，并分析了边界 BFV 算子的性质。此外，我们考虑了混合边界条件，并表明它们会导致量子异常，即（修改后的微分）量子主方程的失败。我们表明可以通过在动作中添加边界项来恢复它，代价​​是在边界算子中引入角项。我们还表明，总状态空间上的量子 Grothendieck BFV 算子是微分的，即平方为零，这对于明确定义的 BV 上同调是必要的。