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}
}
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… 
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References

SHOWING 1-10 OF 69 REFERENCES
Vortex Counting and Lagrangian 3-Manifolds
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. This
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 $SU(2)$,
$ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls
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}}
Chern-Simons theory and S-duality
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, various
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 generator
Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry
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,
AGT on the S-duality wall
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} =
Gauge theory loop operators and Liouville theory
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 theory
SUSY gauge theories on squashed three-spheres
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)
S-duality and 2d topological QFT
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) 6d
...
1
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