# More On Gauge Theory And Geometric Langlands

@article{Witten2015MoreOG, title={More On Gauge Theory And Geometric Langlands}, author={Edward Witten}, journal={arXiv: High Energy Physics - Theory}, year={2015} }

The geometric Langlands correspondence was described some years ago in terms of $S$-duality of $\N=4$ super Yang-Mills theory. Some additional matters relevant to this story are described here. The main goal is to explain directly why an $A$-brane of a certain simple kind can be an eigenbrane for the action of 't Hooft operators. To set the stage, we review some facts about Higgs bundles and the Hitchin fibration. We consider only the simplest examples, in which many technical questions can be… Expand

#### 31 Citations

Quantum $q$-Langlands Correspondence

- Physics, Mathematics
- Transactions of the Moscow Mathematical Society
- 2018

We formulate a two-parameter generalization of the geometric Langlands correspondence, which we prove for all simply-laced Lie algebras. It identifies the q-conformal blocks of the quantum affine… Expand

Supersymmetric field theories and geometric
Langlands: The other side of the coin

- Physics, Mathematics
- Proceedings of Symposia in Pure Mathematics
- 2018

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… Expand

Hecke modifications of Higgs bundles and the extended Bogomolny equation

- Mathematics
- 2019

Abstract We establish a Kobayashi–Hitchin correspondence between solutions of the extended Bogomolny equation with a Dirac type singularity and Hecke modifications of Higgs bundles. This… Expand

Torsion line bundles and branes on the Hitchin system

- Mathematics
- 2018

We study the fixed loci for the action of tensorisation by a line bundle of order $n$ on the moduli space of Higgs bundles for the Langlands self-dual group $\mathrm{GL}(n,\mathbb{C})$. We equip… Expand

S-duality of boundary conditions and the
Geometric Langlands program

- Physics, Mathematics
- Proceedings of Symposia in Pure Mathematics
- 2018

Maximally supersymmetric gauge theory in four dimensions admits local boundary conditions which preserve half of the bulk supersymmetries. The S-duality of the bulk gauge theory can be extended in a… Expand

Green-Schwarz superstring as subsector of Yang-Mills theory

- Physics, Mathematics
- 2015

We consider Yang-Mills theory with N=2 super translation group in ten auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold \Sigma_2\times H^2, where… Expand

Quantum Hall Effect and Langlands Program

- Physics, Mathematics
- Annals of Physics
- 2018

Recent advances in the Langlands program shed light on a vast area of modern mathematics from an unconventional viewpoint, including number theory, gauge theory, representation, knot theory and etc.… Expand

Quantisation conditions of the quantum Hitchin system and the real geometric Langlands correspondence

- Physics, Mathematics
- 2017

Single-valuedness of the eigenfunctions of the quantised Hitchin Hamiltonians is proposed as a natural quantisation condition. Separation of Variables can be used to relate the classification of… Expand

Mirror symmetry for Nahm branes

- Mathematics
- 2017

Using the Dirac--Higgs bundle and the morphism given by tensorization, we consider a new class of virtual hyperholomorphic bundles over the moduli space of M of degree 0 semistable Higgs bundles.… Expand

The reverse Yang–Mills–Higgs flow in a neighbourhood of a critical point

- Mathematics
- 2016

The main result of this paper is a construction of solutions to the reverse Yang-Mills-Higgs flow converging in the $C^\infty$ topology to a critical point. The construction uses only the complex… Expand

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