3-Manifolds and VOA Characters
Miranda C. N. Cheng, Sungbong Chun, Boris Feigin, Francesca Ferrari, Sergei Gukov, Sarah M. Harrison, D. Passaro
Abstract
Abstract By studying the properties of q -series $$\widehat{Z}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Z</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:math> -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 $$\widehat{Z}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Z</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:math> -invariants leads to many infinite families of new fermionic formulae for VOA characters.