Corpus ID: 119220905

From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality

@article{Wu2009FromLT,
  title={From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality},
  author={Jian-feng Wu and Y. Zhou},
  journal={arXiv: High Energy Physics - Theory},
  year={2009}
}
We propose an SL(2,R) Chern-Simons description of Liouville field theory (LFT), whose correlation function duals to partition function of N=2 SU(2) gauge theories. We give the dual expressions for conformal blocks, fusion rules, and Wilson loop operators in Chern-Simons theory. By realizing Wilson loop operator in Liouville as a Hopf link in S^3 on which lives an SL(2,R) Chern-Simons theory, we obtain an alternative description of monodromy of this loop operator in Liouville field theory as the… Expand

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References

SHOWING 1-10 OF 71 REFERENCES
Operator formalism for Chern-Simons theories
Abstract The operator formalism for Chern-Simons theories with gauge group G and parameter k (G=U(1), SU(2)) on an arbitrary oriented compact three-dimensional manifold is constructed. The states ofExpand
Loop operators and S-duality from curves on Riemann surfaces
We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify allExpand
Inducing Liouville theory from topologically massive gravity
Abstract The well-known relationship between three-dimensional Chern-Simons theories and two-dimensional Wess-Zumino-Witten models may be understood as a straightforward consequence of symmetryExpand
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 theoryExpand
A Note on Wilson Loop in N=2 Quiver/M theory Gravity Duality
We study Wilson loops in the 4-dimensional N=2 supersymmetric quiver/M theory duality recently constructed by Gaiotto and Maldacena, that is conjectured to be dual to M2 branes on AdS_5\times S^4Expand
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,Expand
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) 6dExpand
Notes on the verlinde formula in nonrational conformal field theories
We review and extend evidence for the validity of a generalized Verlinde formula, in particular, nonrational conformal field theories. We identify a subset of representations of the chiral algebra inExpand
Hitchin systems, N = 2 gauge theories and W-gravity
Abstract We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N = 2Expand
Global charges in Chern-Simons theory and the 2+1 black hole.
  • Bañados
  • Physics, Medicine
  • Physical review. D, Particles and fields
  • 1995
TLDR
It is proved that for diffeomorphisms that do not preserve the boundary there is a classical contribution to the central charge in the Virasoro algebra. Expand
...
1
2
3
4
5
...