Séminaire de Physique Théorique

3d gauge theories from homological knot invariants

by Prof. Piotr SULKOWSKI (University of Warsaw & Caltech)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


IHES Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Compactifications of M5-branes on non-trivial 3-manifolds lead to a N=2 supersymmetric theories in 3 dimensions. If the 3-manifold in question is a knot complement, various Chern-Simons amplitudes - or corresponding knot invariants - for this knot determine the properties of the resulting 3d, N=2 theory. This relation between N=2 theories and Chern-Simons theory is referred to as the 3d-3d correspondence. M-theory realization of this correspondence implies that N=2 theories obtained in this way possess one special flavor symmetry, which is related to certain deformation of Chern-Simons theory and homological knot invariants. In this talk I will discuss properties of these refined/homological invariants, and their role in the 3d-3d correspondence.