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arXiv · 2201.04640

3-Manifolds and VOA Characters

Miranda C. N. Cheng·Sungbong Chun·Boris Feigin·Francesca Ferrari·Sergei Gukov·Sarah M. Harrison·Davide Passaro
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Abstract

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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Miranda C. N. Cheng, Sungbong Chun, Boris Feigin, Francesca Ferrari, Sergei Gukov, Sarah M. Harrison, Davide Passaro. 2022-01-12. 3-Manifolds and VOA Characters. https://arxiv.org/abs/2201.04640

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