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

## TL;DR

This paper explores the deep connections between various approaches to the geometric Langlands program, linking conformal field theory, supersymmetric gauge theories, and surface operators through advanced mathematical physics frameworks.

## Contribution

It unifies different perspectives on the geometric Langlands correspondence, revealing its relation to the AGT-correspondence and surface operators via sigma models and Hitchin moduli spaces.

## Key findings

- Geometric Langlands as Nekrasov-Shatashvili limit of AGT with surface operators
- Interpretation of the correspondence through 2D sigma models and Hitchin spaces
- Connections between conformal field theory, supersymmetric gauge theories, and geometric Langlands

## Abstract

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. The geometric Langlands correspondence is described as the Nekrasov-Shatashvili limit of a generalisation of the AGT-correspondence in the presence of surface operators. Following the approaches of Kapustin - Witten and Nekrasov - Witten we interpret some aspects of the resulting picture using an effective description in terms of two-dimensional sigma models having Hitchin's moduli spaces as target-manifold.