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arXiv · 1108.4389

Gauge Theories Labelled by Three-Manifolds

Tudor Dimofte·Davide Gaiotto·Sergei Gukov
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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.

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Tudor Dimofte, Davide Gaiotto, Sergei Gukov. 2011-08-22. Gauge Theories Labelled by Three-Manifolds. https://arxiv.org/abs/1108.4389

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