Speaker
Description
This talk will report on recent developments at the intersection of QFT and low-dimensional topology. WRT invariants of 3-manifolds were conjectured by Gukov-Pei-Putrov-Vafa to admit a refinement and generalization known as Z-hat invariants, motivated by 3d-3d correspondence. In following work, Gukov and Manolescu introduced a generalization of Z-hat for knot complements. By the Lickorish-Wallance theorem these can be regarded as more fundamental building blocks for Z-hat of closed 3-manifolds, which can be recovered by surgery formulae. In this talk I will present a first-principles computation of the Gukov-Manolescu invariant for (2,2p+1) torus knots. The derivation is based on the duality between Chern-Simons gauge theory and A-model open topological strings, and hinges on a localization technique for counting holomorphic curves on the knot complement. The formula that we obtain corresponds to the open topological string partition function in the resolved conifold with a Lagrangian brane supported on the knot complement. The technique developed in this work applies more generally to all fibered knots. Based on joint works with S. Chauhan and T. Ekholm.