1. 3-Manifolds and VOA Characters
- Author
-
Cheng, Miranda C. N., Chun, Sungbong, Feigin, Boris, Ferrari, Francesca, Gukov, Sergei, Harrison, Sarah M., and Passaro, Davide
- Subjects
High Energy Physics - Theory ,Mathematics - Geometric Topology ,Mathematics - Quantum Algebra ,Mathematics - Representation Theory - 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., Comment: 85 pages, 3 figures, 6 tables
- Published
- 2022