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Gauge Theories Labelled by Three-Manifolds

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Abstract

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.

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Authors and Affiliations

  1. Institute for Advanced Study, Einstein Dr., Princeton, NJ, 08540, USA

    Tudor Dimofte & Davide Gaiotto

  2. California Institute of Technology, Pasadena, CA, 91125, USA

    Sergei Gukov

  3. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Sergei Gukov

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  1. Tudor Dimofte
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  2. Davide Gaiotto
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  3. Sergei Gukov
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Correspondence to Tudor Dimofte.

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Communicated by N. A. Nekrasov

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Dimofte, T., Gaiotto, D. & Gukov, S. Gauge Theories Labelled by Three-Manifolds. Commun. Math. Phys. 325, 367–419 (2014). https://doi.org/10.1007/s00220-013-1863-2

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