3-流形与VOA特征标
3-Manifolds and VOA Characters
摘要：
通过研究$q$ -系列$\widehat Z$ -不变量的性质，我们建立了一个3-流形与顶点代数之间的字典.特别是，我们将以前已知的条目在这本字典中的李群的更高的排名，3-流形与toral边界，和BPS配分函数与线运营商。这在3d-3d对应的框架下为对数顶点代数提供了一种新的物理实现，并为今后的研究开辟了新的途径。例如，我们说明了如何调用一个结的对应$\widehat{Z}$ -不变量导致许多新的费米子公式的VOA字符的无限家庭。
英文摘要：
By studying the properties of $q$-series $\widehat Z$-invariants, we develop a dictionary between 3-manifolds and vertex algebras. In particular, we generalize previously known entries in this dictionary to Lie groups of higher rank, to 3-manifolds with toral boundaries, and to BPS partition functions with line operators. This provides a new physical realization of logarithmic vertex algebras in the framework of the 3d-3d correspondence and opens new avenues for their future study. For example, we illustrate how invoking a knot-quiver correspondence for $\widehat{Z}$-invariants leads to many infinite families of new fermionic formulae for VOA characters.
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