Gauge Theories Labelled by ThreeManifolds
Abstract
We propose a dictionary between geometry of triangulated 3manifolds and physics of threedimensional gauge theories. Under this duality, standard operations on triangulated 3manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independence of the SL(2) ChernSimons partition function on the choice of triangulation translates to a statement that partition functions of two mirror 3d gauge theories are equal. Threedimensional field theories associated to 3manifolds can be thought of as theories that describe boundary conditions and duality walls in fourdimensional SCFTs, thus making the whole construction functorial with respect to cobordisms and gluing.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 January 2014
 DOI:
 10.1007/s0022001318632
 Bibcode:
 2014CMaPh.325..367D