# Gauge Theory and Langlands Duality

@article{Frenkel2009GaugeTA, title={Gauge Theory and Langlands Duality}, author={Edward Vladimir Frenkel}, journal={arXiv: Representation Theory}, year={2009} }

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…

## 42 Citations

A Physics Perspective on Geometric Langlands Duality

- Mathematics
- 2010

We review the approach to the geometric Langlands program for algebraic curves via S-duality of an N = 4 supersymmetric four-dimensional gauge theory, initiated by Kapustin and Witten in 2006. We…

Quantum Langlands dualities of boundary conditions, $D$-modules, and conformal blocks

- MathematicsCommunications in Number Theory and Physics
- 2020

We review and extend the vertex algebra framework linking gauge theory constructions and a quantum deformation of the Geometric Langlands Program. The relevant vertex algebras are associated to…

Quantum $q$-Langlands Correspondence

- MathematicsTransactions 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…

Langlands Program, Trace Formulas, and their Geometrization

- Mathematics
- 2012

The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the…

Questions and remarks to the Langlands programme

- Mathematics
- 2012

A brief survey is given of the classical Langlands programme to construct a correspondence between n-dimensional representations of Galois groups of local and global fields of dimension 1 and…

Local Langlands Duality and a Duality of Conformal Field Theories

- Mathematics
- 2015

We show that the numerical local Langlands duality for GL_n and the T - duality of two-dimensional quantum gravity arise from one and the same symmetry principle. The unifying theme is that the local…

J un 2 01 5 Local Langlands Duality and a Duality of Conformal Field Theories

- Mathematics
- 2018

We show that the numerical local Langlands duality for GLn and the T – duality of twodimensional quantum gravity arise from one and the same symmetry principle. The unifying theme is that the local…

Landscaping with fluxes and the E8 Yukawa Point in F-theory

- Mathematics
- 2014

Integrality in the Hodge theory of Calabi-Yau fourfolds is essential to nd the vacuum structure and the anomaly cancellation mechanism of four dimensional F-theory compactications. We use the…

Some aspects of abelian and nonabelian T-duality and the gauge/gravity correspondence

- Mathematics
- 2016

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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