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Gauge Theories Labelled by Three-Manifolds
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Gauge Theories Labelled by Three-Manifolds
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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.
Forward citations
Cited by 7 Pith papers
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Half-BPS Boundaries and the RG-Wall of $\mathcal{N}=2$ $SU(N)$ SYM
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Meromorphic amplitudes from 3-dimensional supersymmetry
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Gang-Kim-Yoon integrality conjectures on adjoint Reidemeister torsions for torus knots
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