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3d Gauge Theories Labelled by 3-Manifolds

Hold Date
2012-03-10 14:00〜2012-03-10 16:30
Seminar Room 7, Faculty of Mathematics building, Ito Campus
Object person
Tudor Dimofte (IAS, Princeton)

The lecturer comments on the subject of arXiv:1108.4389, 1112.5179.

We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N=2 gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independence of the SL(2) Chern-Simons partition function on the choice of triangulation translates to a statement that S^3_b partition functions of two mirror 3d N=2 gauge theories are equal. Three-dimensional N=2 field theories associated to 3-manifolds can be thought of as theories that describe boundary conditions and duality walls in four-dimensional N=2 SCFTs, thus making the whole construction functorial with respect to cobordisms and gluing.