Gauge Theories Labelled by Three-Manifolds
Abstract
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.
Keywords
Cite
@article{arxiv.1108.4389,
title = {Gauge Theories Labelled by Three-Manifolds},
author = {Tudor Dimofte and Davide Gaiotto and Sergei Gukov},
journal= {arXiv preprint arXiv:1108.4389},
year = {2011}
}
Comments
59 pages, 24 figures