A large class of supersymmetric quantum field theories, including all theories with $${\mathcal {N}}= 2$$ N = 2 supersymmetry in three dimensions and theories with $${\mathcal {N}}= 2$$ N = 2 supersymmetry in four dimensions, possess topological–holomorphic sectors. We formulate Poisson vertex algebras in such topological–holomorphic sectors and discuss some examples. For a four-dimensional $${\mathcal {N}}= 2$$ N = 2 superconformal field theory, the associated Poisson vertex algebra is the classical limit of a vertex algebra generated by a subset of local operators of the theory.

中文翻译：

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超对称场论中的泊松顶点代数

一大类超对称量子场论，包括所有$${\mathcal {N}}= 2$$ N = 2 三维超对称的理论和$${\mathcal {N}}= 2$$ N的理论= 2 四维超对称，具有拓扑全纯扇区。我们在这样的拓扑全纯扇区中制定泊松顶点代数并讨论一些例子。对于四维 $${\mathcal {N}}= 2$$ N = 2 超共形场论，相关的泊松顶点代数是由该理论的局部算子子集生成的顶点代数的经典极限。