Gauge Theories Labelled by Three-Manifolds

2011/08/22 by Tudor Dimofte, Dimofte, Tudor, Davide Gaiotto +3 · 10 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1108.4389

openalex publication_date 2011/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S³_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.

Citations

• 2 + 1 dimensional gravity as an exactly soluble system
• Wall-crossing, Hitchin Systems, and the WKB Approximation

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