3Manifolds and VOA Characters
Abstract
By studying the properties of $q$series $\widehat Z$invariants, we develop a dictionary between 3manifolds and vertex algebras. In particular, we generalize previously known entries in this dictionary to Lie groups of higher rank, to 3manifolds 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 3d3d correspondence and opens new avenues for their future study. For example, we illustrate how invoking a knotquiver correspondence for $\widehat{Z}$invariants leads to many infinite families of new fermionic formulae for VOA characters.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 DOI:
 10.48550/arXiv.2201.04640
 arXiv:
 arXiv:2201.04640
 Bibcode:
 2022arXiv220104640C
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Geometric Topology;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 85 pages, 3 figures, 6 tables