English

Gauge Theories Labelled by Three-Manifolds

High Energy Physics - Theory 2011-08-23 v1 Geometric Topology Quantum Algebra

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