Lectures on the Langlands Program and Conformal Field Theory

TL;DR

This paper provides an accessible overview of recent advances in the geometric Langlands correspondence and its connections to conformal field theory, highlighting potential applications in quantum field theory.

Contribution

It offers a self-contained introduction to the geometric Langlands Program and explores its recent links to two-dimensional conformal field theory, aimed at physicists.

Findings

Connections between Langlands duality and conformal field theory elucidated

Potential applications of geometric Langlands in quantum field theory discussed

Recent results in geometric Langlands summarized

Abstract

These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric reformulation, addressed primarily to physicists. I tried to make it as self-contained as possible, requiring very little mathematical background. Next, we describe the connections between the Langlands Program and two-dimensional conformal field theory that have been found in the last few years. These connections give us important insights into the physical implications of the Langlands duality.