String Theory Journal Club

The goal of this talk is to present a new set of symmetries for colored HOMFLY-PT knot invariants and their implications as dualities in the 3d - 3d correspondence. These are the results of joint work with Piotr Sułkowski, Jakub Jankowski, Piotr Kucharski and Dmitry Noshchenko. For the overture, we will review how the set of 3d N = 2 gauge theories arising from string compactification can be described in terms of a quiver diagram (directed graph). We will use scalar QED as the simplest example. Then, in the intermezzo, we will see how dualities between 3d theories naturally arise from operations on the quiver diagram. These operations are manifestations of the pentagon identity for the quantum dilogarithm. For our gran finalle, we will find that these dualities for certain quivers lead to new symmetries for knot invariants. Link: meet.google.com/gbj-tmns-err