Lectures on the Langlands Program and Conformal Field Theory

2005/12/15 by Edward Frenkel, Frenkel, Edward · 5 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.hep-th/0512172

openalex publication_date 2005/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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