# Gauge Theories Labelled by Three-Manifolds

@article{Dimofte2011GaugeTL,
title={Gauge Theories Labelled by Three-Manifolds},
author={Tudor Dan Dimofte and Davide Gaiotto and Sergei Gukov},
journal={Communications in Mathematical Physics},
year={2011},
volume={325},
pages={367-419}
}
• Published 22 August 2011
• Physics, Mathematics
• Communications in Mathematical Physics
We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional $${\mathcal{N} = 2}$$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 $${S^{3}_{b}}$$Sb3 partition functions of two… Expand
351 Citations
Three-dimensional gauge theories with supersymmetry enhancement
• Physics
• Physical Review D
• 2018
We conjecture infrared emergent $\mathcal{N}=4$ supersymmetry for a class of three-dimensional $\mathcal{N}=2$ $U(1)$ gauge theories coupled with a single chiral multiplet. One example is the caseExpand
Supersymmetric partition functions and the three-dimensional A-twist
• Physics
• 2017
A bstractWe study three-dimensional N=2$$\mathcal{N}=2$$ supersymmetric gauge theories on ℳg,p$${\mathrm{\mathcal{M}}}_{g,p}$$, an oriented circle bundle of degree p over a closed RiemannExpand
Boundaries, mirror symmetry, and symplectic duality in 3d N=4$$\mathcal{N}=4$$ gauge theory
• Physics, Mathematics
• 2016
A bstractWe introduce several families of N=2,2$$\mathcal{N}=\left(2,\ 2\right)$$ UV boundary conditions in 3d N=4$$\mathcal{N}=4$$Expand
Refined 3d-3d correspondence
• Physics
• 2017
A bstractWe explore aspects of the correspondence between Seifert 3-manifolds and 3d N$$\mathcal{N}$$ = 2 supersymmetric theories with a distinguished abelian flavour symmetry. We give aExpand
Abelian dualities of $$\mathcal{N}$$ = (0, 4) boundary conditions
• T. Okazaki
• Physics
• Journal of High Energy Physics
• 2019
Abstract We propose dual pairs of $$\mathcal{N}$$ N = (0, 4) half-BPS boundary conditions for 3d $$\mathcal{N}$$ N = 4 Abelian gauge theories related to mirror symmetryExpand
BPS spectra and 3-manifold invariants
• Physics, Mathematics
• 2017
We provide a physical definition of new homological invariants $\mathcal{H}_a (M_3)$ of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in questionExpand
Large N twisted partition functions in 3d-3d correspondence and holography
• Physics
• Physical Review D
• 2019
We study the large $N$ limit of twisted partition functions on $\mathcal{M}_{g,p}$, the $S^1$ bundle of degree $p$ over a Riemann surface of genus $g$, for 3D $\mathcal{N}=2$ superconformal fieldExpand
Quiver gauge theories and integrable lattice models
A bstractWe discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). TheExpand
4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block
A bstractA class of 3d N=2$$\mathcal{N}=2$$ supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applyingExpand
An N=1$$\mathcal{N}=1$$ 3d-3d correspondence
• Physics
• Journal of High Energy Physics
• 2018
A bstractM5-branes on an associative three-cycle M3 in a G2-holonomy manifold give rise to a 3d N=1$$\mathcal{N}=1$$ supersymmetric gauge theory, TN=1M3$${T}_{\mathcal{N}=1}\left[{M}_3\right]$$.Expand

#### References

SHOWING 1-10 OF 68 REFERENCES
Vortex Counting and Lagrangian 3-Manifolds
• Mathematics, Physics
• 2011
To every 3-manifold M one can associate a two-dimensional $${\mathcal{N}=(2, 2)}$$ supersymmetric field theory by compactifying five-dimensional $${\mathcal{N}=2}$$ super-Yang–Mills theory on M. ThisExpand
Quantum Riemann Surfaces in Chern-Simons Theory
We construct from first principles the operators $\hat A_M$ that annihilate the partition functions (or wavefunctions) of three-dimensional Chern-Simons theory with gauge groups $SU(2)$,Expand
${\text{SL}}\left( {2,\mathbb{R}} \right)$ Chern-Simons, Liouville, and gauge theory on duality walls
• Physics, Mathematics
• 2011
We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d ${\text{SL}}\left( {2,\mathbb{R}}Expand Chern-Simons theory and S-duality • Physics, Mathematics • 2011 A bstractWe study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, variousExpand SL(2;Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry On the space of three-dimensional conformal field theories with U(1) symmetry and a chosen coupling to a background gauge field, there is a natural action of the group$SL(2,{\bf Z})$. The generatorExpand Loop and surface operators in$ \mathcal{N} = 2 $gauge theory and Liouville modular geometry • Physics • 2010 Recently, a duality between Liouville theory and four dimensional$ \mathcal{N} = 2 $gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory,Expand AGT on the S-duality wall • Physics • 2010 Three-dimensional gauge theory T [G] arises on a domain wall between four-dimensional$ \mathcal{N} = 4 $SYM theories with the gauge groups G and its S-dual GL. We argue that the$ \mathcal{N} =Expand
Gauge theory loop operators and Liouville theory
• Physics
• 2009
We propose a correspondence between loop operators in a family of four dimensional $$\mathcal{N}$$ = 2 gauge theories on S4 — including Wilson, ‘t Hooft and dyonic operators — and Liouville theoryExpand
SUSY gauge theories on squashed three-spheres
• Physics
• 2011
We study Euclidean 3D $\mathcal{N} = 2$ supersymmetric gauge theories on squashed three-spheres preserving isometries SU(2) × U(1) or U(1) × U(1). We show that, when a suitable background U(1)Expand
S-duality and 2d topological QFT
• Physics
• 2010
We study the superconformal index for the class of $$\mathcal{N} = 2$$ 4d superconformal field theories recently introduced by Gaiotto [1]. These theories are defined by compactifying the (2, 0) 6dExpand