arXiv 2211.044102022-11hep-th

4d N=2 超共形场论中扩展算子的顶点代数

Vertex algebra of extended operators in 4d N=2 superconformal field theories

Philip C. Argyres, Matteo Lotito, Mitch Weaver

备注：: V3: 46 pages, 2 figures; minor corrections, fixed typeset errors, added references, added comments on computing descent operator OPEs in generic SCFTs at the end of section 4; matches version to be published in JHEP

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AI总结：

本文在4d N=2超共形场论中，通过拓扑下降从Schur算子构造扩展算子，证明其扩大顶点算子代数，并以自由超多重态为例计算扩展算子乘积展开。

摘要：

我们在4d N=2超共形场论（SCFTs）的一对扭曲Schur超荷的上同调中构造了一类扩展算子。这些扩展算子是通过拓扑下降（topological descent）方法，由该上同调中的局域算子——即Schur算子——构造而来。它们是Schur算子的某些超后代（super descendants）的线、面和畴壁世界体积积分。其世界体积在闵可夫斯基时空中沿垂直于某一空间平面的方向延伸。作为这些扭曲Schur超荷上同调中的算子，它们的关联函数（局域地）仅是关于它们与该平面相交位置的全纯函数。这意味着扩展算子扩大了Schur算子的顶点算子代数。我们通过计算自由超多重态SCFT中该代数的一个子代数内的某些扩展算子乘积展开（extended-operator product expansions）来阐明这个扩大的顶点代数。

英文摘要：

We construct a class of extended operators in the cohomology of a pair of twisted Schur supercharges of 4d N=2 SCFTs. The extended operators are constructed from the local operators in this cohomology -- the Schur operators -- by a version of topological descent. They are line, surface, and domain wall world volume integrals of certain super descendants of Schur operators. Their world volumes extend in directions transverse to a spatial plane in Minkowski space-time. As operators in the cohomology of these twisted Schur supercharges, their correlators are (locally) meromorphic functions only of the positions where they intersect this plane. This implies the extended operators enlarge the vertex operator algebra of the Schur operators. We illustrate this enlarged vertex algebra by computing some extended-operator product expansions within a subalgebra of it for the free hypermultiplet SCFT.

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