• Corpus ID: 2338737

Gauge Theory and Langlands Duality

@article{Frenkel2009GaugeTA,
  title={Gauge Theory and Langlands Duality},
  author={Edward Vladimir Frenkel},
  journal={arXiv: Representation Theory},
  year={2009}
}
  • E. Frenkel
  • Published 15 June 2009
  • Mathematics
  • arXiv: Representation Theory
The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories of sheaves on moduli spaces of (flat) bundles on algebraic curves. Three years ago, in a groundbreaking advance, Kapustin and Witten have linked the geometric Langlands correspondence to the S-duality of 4D supersymmetric gauge theories. This and subsequent… 
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42 Citations
Background Citations
14
Methods Citations
2

42 Citations

Citation Type

Citation Type

A Physics Perspective on Geometric Langlands Duality
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J un 2 01 5 Local Langlands Duality and a Duality of Conformal Field Theories
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In this thesis we study properties of type II supergravity solutions generated by abelian and nonabelian T-duality. Also we determine, through the gauge/gravity conjecture, some aspects of the eld…
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References

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Montonen-Olive duality implies that the categories of A-branes on the moduli spaces of Higgs bundles on a Riemann surface C for a pair of Langlands-dual groups are equivalent. We reformulate this as…
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  • E. Witten
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2010
Geometric Langlands duality relates a representation of a simple Lie group Gv to the cohomology of a certain moduli space associated with the dual group G. In this correspondence, a principal SL2…
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TLDR
Yang-Mills S-duality makes predictions for all correlators of this effective conformal field theory that Montonen-Olive duality between electric and magnetic states reduces to the standard two-dimensionalDuality between momentum and winding states.
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