String-Math Seminar: Dualities in Topological Field Theory

Seminar | April 10 | 2-3 p.m. | 402 LeConte Hall

 Constantin Teleman, Berkeley

 Department of Mathematics

Kramers-Wannier duality is a symmetry relating the high-and low-temperature phases of the 2-dimensional lattice Ising model. Electric-Magnetic duality is a 3-dimensional duality between abelian (flat) gauge theories for Pontryagin dual abelian groups. Both dualities generalize to higher-dimensional manifolds. We describe the relation between them using the notion of relative field theory. The order and disorder operators of the Ising model are endpoints of Wilson and t’Hooft electro-magnetic loops, respectively. There is a higher-dimensional generalization to finite homotopy types. This is based on joint work with Dan Freed.