Hélder Larraguível (Uniwersytet Warszawski)

Who put a knot in my 3d N = 2 supersymmetric gauge theory?

At first sight no one would imagine that computing the index of the 3d N = 2 SUSY theory would yield knot invariants, but surprisingly it does! Not only that, the 3d index allowed us to obtain explicit expressions for several knot invariants arising from Chern-Simons theory, which were unknown before! How could that be? First discovered in topological string theory, the duality between 3d Chern-Simons theory and 3d N = 2 SUSY has even introduced new knot invariants, with physical interpretation of BPS particles, or open Gromov-Witten invariants. Given the central role of this duality, I will initially discuss the opposite direction, what other knot invariants teach us about 3d N = 2 SUSY. Then, I will present the results of ongoing effort with my collaborators towards understanding why many distinct 3d N = 2 SUSY theories have the same knot, and how many are they.