Communications in Mathematical Physics

, Volume 325, Issue 2, pp 367–419 | Cite as

Gauge Theories Labelled by Three-Manifolds

  • Tudor DimofteEmail author
  • Davide Gaiotto
  • Sergei Gukov


We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional \({\mathcal{N} = 2}\) 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 \({\mathcal{N} = 2}\) gauge theories are equal. Three-dimensional \({\mathcal{N} = 2}\) field theories associated to 3-manifolds can be thought of as theories that describe boundary conditions and duality walls in four-dimensional \({\mathcal{N} = 2}\) SCFTs, thus making the whole construction functorial with respect to cobordisms and gluing.


Gauge Theory Partition Function Modulus Space Coulomb Branch Chiral Multiplet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.California Institute of TechnologyPasadenaUSA
  3. 3.Max-Planck-Institut für MathematikBonnGermany

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