顶点算子超代数的Kazhdan-Lusztig对应关系：从阿贝尔规范理论的拓扑B扭中获得
Kazhdan-Lusztig Correspondence for Vertex Operator Superalgebras from Abelian Gauge Theories
AI总结：
本文通过拓扑B扭的阿贝尔规范理论边界VOA，证明了顶点算子超代数的Kazhdan-Lusztig对应关系，并将线缺陷视为Hopf代数模块，同时验证了Semikhatov-Tipunin猜想的一个案例。
摘要：
我们证明了一类顶点算子超代数的Kazhdan-Lusztig对应关系，这些代数通过Costello-Gaiotto的工作作为三维N=4阿贝尔规范理论的拓扑B扭边界VOA出现。这意味着我们展示了特定仿射顶点超代数模块的辫状张量范畴与相应量子超群的等价关系。我们基于Creutzig-Lentner-Rupert的工作扩展了这一大类VOA，因为在我们的案例中这些范畴没有项目对象，对象可以有任意Jordan-Hölder长度。我们的对应关系显著提升了对这一类TQFT相关线缺陷辫状张量范畴的理解，通过将线缺陷视为Hopf代数的模块。在此过程中，我们证明了Semikhatov-Tipunin猜想的一个案例，将对数CFT与筛选算子的Nichols代数联系起来。
英文摘要：
We prove the Kazhdan-Lusztig correspondence for a class of vertex operator superalgebras which, via the work of Costello-Gaiotto, arise as boundary VOAs of topological B twist of 3d $\mathcal{N}=4$ abelian gauge theories. This means that we show equivalences of braided tensor categories of modules of certain affine vertex superalgebras and corresponding quantum supergroups. We build on the work of Creutzig-Lentner-Rupert to this large class of VOAs and extend it since in our case the categories don't have projective objectives and objects can have arbitrary Jordan Hölder length. Our correspondence significantly improves the understanding of the braided tensor category of line defects associated to this class of TQFT, by realizing line defects as modules of a Hopf algebra. In the process, we prove a case of the conjecture of Semikhatov-Tipunin, relating logarithmic CFTs to Nichols algebras of screening operators.
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