• Corpus ID: 245906254

3-Manifolds and VOA Characters

@inproceedings{Cheng20223ManifoldsAV,
  title={3-Manifolds and VOA Characters},
  author={Miranda C N Cheng and Sungbong Chun and Boris Feigin and Francesca Ferrari and Sergei Gukov and Sarah M. Harrison and Davide Passaro},
  year={2022}
}
By studying the properties of q-series Ẑ-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… 

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References

SHOWING 1-10 OF 91 REFERENCES
Non-semisimple TQFT's and BPS q-series
We propose and in some cases prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic $q$. Both types of invariants are labeled by extra
Fivebranes and 3-manifold homology
A bstractMotivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of
Rozansky–Witten invariants via Atiyah classes
Recently, L. Rozansky and E. Witten associated to any hyper-Kähler manifold X a system of ‘weights’ (numbers, one for each trivalent graph) and used them to construct invariants of topological
Quantum modular forms and plumbing graphs of 3-manifolds
Fivebranes and 4-manifolds
We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2) theories, we obtain a number of results, which
Rozansky-Witten invariants via formal geometry
We show that recently constructed invariants of 3-dimensional manifolds and of hyperkaehler manifolds (L.Rozansky and E.Witten, hep-th/9612216) come from characteristic classes of foliations and from
Hyper-Kähler geometry and invariants of three-manifolds
Abstract We study a 3-dimensional topological sigma-model, whose target space is a hyper-Kähler manifold X. A Feynman diagram calculation of its partition function demonstrates that it is a finite
W-algebras , false theta functions and quantum modular forms
In this paper, we study certain partial and false theta functions in connection to vertex operator algebras and conformal field theory. We prove a variety of results concerning the asymptotics of
...
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