Gauge Theories Labelled by Three-Manifolds

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.

59 pages, 24 figures

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Cited by in corpus (32)

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• Higgs branch localization in three dimensions
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Line operators on S^1xR^3 and quantization of the Hitchin moduli space
• Seiberg-like Dualities for 3d N=2 Theories with SU(N) gauge group
• Dynamics of 3D SUSY Gauge Theories with Antisymmetric Matter
• The general M5-brane superconformal index
• Quarter-BPS AdS5 solutions in M-theory with a T2 bundle over a Riemann surface
• Superconformal Index with Duality Domain Wall
• New Directions in Bipartite Field Theories
• Toda Theory From Six Dimensions
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• A 5d/3d duality from relativistic integrable system
• A new pentagon identity for the tetrahedron index
• Network, Cluster coordinates and N=2 theory I
• 4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area
• BPS spectrum, wall crossing and quantum dilogarithm identity
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• The symplectic properties of the PGL(n,C)-gluing equations
• 6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
• Localization principle in SUSY gauge theories
• Static Charges in the Low-Energy Theory of the S-Duality Twist
• BPS states in the Omega-background and torus knots
• Flows between Dualities for 3d Chern-Simons Theories
• Super-A-polynomial
• Tangles, Generalized Reidemeister Moves, and Three-Dimensional Mirror Symmetry
• Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions
• A generating series for Murakami-Ohtsuki-Yamada graph evaluations