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This note announces results on the relations between the approach of Beilinson and Drinfeld to the geometric Langlands correspondence based on conformal field theory, the approach of Kapustin and Witten based on $N=4$ SYM, and the AGT-correspondence.
N. J. Hitchin, The self-duality equations on a Riemann surface
1987
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S. Cecotti and C. Vafa, Topological antitopological fusion
1991
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B. Feigin and E. Frenkel, Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras
1992
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C. Simpson, Higgs bundles and local systems
1992
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A. Braverman, Instanton counting via affine Lie algebras. 1. Equivariant J functions of (affine) flag manifolds and Whittaker vectors
2004
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Providence, USA: Am. Math. Soc. (2004) 400 p, 2004
E. Frenkel and D. Ben-Zvi, Vertex algebras and algebraic curves · 2004
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A. Kapustin and E. Witten, Electric-Magnetic Duality And The Geometric Langlands Program
2007
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Springer Berlin Heidelberg, Berlin, Heidelberg, 2007
E. Frenkel, Lectures on the Langlands Program and Conformal Field Theory · 2007
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D. Gaiotto and E. Witten, Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
2009
Earlier work this paper cites.
D. Gaiotto and E. Witten, S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
2009
Earlier work this paper cites.
2009
Earlier work this paper cites.
N. A. Nekrasov and S. L. Shatashvili, Quantization of Integrable Systems and Four Dimensional Gauge Theories · 2009
Earlier work this paper cites.
2010
Earlier work this paper cites.
N. Nekrasov and E. Witten, The Omega Deformation, Branes, Integrability, and Liouville Theory
2010
Cited alongside, same era.
L. F. Alday and Y. Tachikawa, Affine SL(2) conformal blocks from 4d gauge theories
2010
Cited alongside, same era.
E. Frenkel, On the brane interpretation of conformal blocks
2010
Cited alongside, same era.
2010
Cited alongside, same era.
N. Drukker, J. Gomis, T. Okuda, and J. Teschner, Gauge Theory Loop Operators and Liouville Theory
2010
Cited alongside, same era.
D. Gaiotto, G. W. Moore, and A. Neitzke, Wall-crossing, Hitchin systems, and the WKB approximation
2013
Later among the works it cites.
D. Arinkin and D. Gaitsgory, Singular support of coherent sheaves and the geometric Langlands conjecture
2015
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D. Gaitsgory, Outline of the proof of the geometric Langlands conjecture for G L 2 GL_{2}
2015
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S. Nawata, Givental J-functions, Quantum integrable systems, AGT relation with surface operator
2015
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2015
Later among the works it cites.
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2011
Cited alongside, same era.
2011
Cited alongside, same era.
2011
Cited alongside, same era.
D. Gaiotto and E. Witten, Knot Invariants from Four-Dimensional Gauge Theory
2012
Cited alongside, same era.
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
2012
Cited alongside, same era.
E. Witten, Fivebranes and knots
2012
Cited alongside, same era.
D. Gaiotto, Surface Operators in N = 2 4d Gauge Theories
2012
Cited alongside, same era.
2015
Later among the works it cites.
D. Honda and T. Okuda, Exact results for boundaries and domain walls in 2d supersymmetric theories
2015
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N. Nekrasov, BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
2016
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D. Arinkin, Irreducible connections admit generic oper structures
2016
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D. Ben-Zvi and D. Nadler, Betti Geometric Langlands
2016
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E. Frenkel, S. Gukov, and J. Teschner, Surface Operators and Separation of Variables
2016
Later among the works it cites.
2016
Later among the works it cites.