GP Seminar: Exploring Z-hat invariant for SO(3), OSp(1|2), and SU(N)/Z_m groups via Gukov-Pei-Putrov-Vafa (GPPV) conjecture

Abstract: Z-hat is a q-series valued topological invariant of three-manifolds predicted via physics of 3d-3d correspondence. Further, the GPPV conjecture is a relation between Witten-Reshetikhin-Turaev (WRT) invariant and Z-hat invariant for a closed three-manifold. Although Z-hat invariants lack a mathematical definition for a general three-manifold, they have been defined for negative-definite plumbed three-manifolds, surgeries on all positive braid links, fibered knots up to ten crossings, and homogeneous braid links.

In this talk, we will limit ourselves to the case of a negative-definite plumbed three-manifold and will define the corresponding Z-hat for SO(3), OSp(1|2), and SU(N)/Z_m groups. In particular, we will set up the WRT invariants for the corresponding groups, followed by analytic continuation within a unit disk to obtain the Z-hat invariants for the corresponding groups.

This is a seminar in our seminar series on Geometry and Physics (GP).