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

Abstract

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 ratio of link invariants. We show how to calculate t'Hooft loops in the simplest example -- the N=4 super Yang-Mills theory. The results we obtained are consistant with those in 0909.0945 and 0909.1105.

26 pages, 5 figures, references added

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• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• Proving AGT conjecture as HS duality: extension to five dimensions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Towards a proof of AGT conjecture by methods of matrix models
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Check of AGT Relation for Conformal Blocks on Sphere
• A slow review of the AGT correspondence
• Supersymmetric AdS3 X S2 M-theory geometries with fluxes
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• N=2 Generalized Superconformal Quiver Gauge Theory
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• N = 2 SCFTs: An M5-brane perspective