Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I

2010/05/17 by J. Teschner, Teschner, J.
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1005.2846

openalex publication_date 2010/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the relation between Liouville theory and the Hitchin integrable system, which can be seen in two ways as a two step process involving quantization and hyperkaehler rotation. The modular duality of Liouville theory and the relation between Liouville theory and the SL(2)-WZNW-model give a new perspective on the geometric Langlands correspondence and on its relation to conformal field theory.

Citations

• A relation between the Knizhnik--Zamolodchikov and Belavin--Polyakov--Zamolodchikov systems of partial differential equations
• The Self-Duality Equations on a Riemann Surface
• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• Twisted Whittaker model and factorizable sheaves
• Liouville Correlation Functions from Four-Dimensional Gauge Theories
• Wall-crossing, Hitchin Systems, and the WKB Approximation

Related

• Classical limit of the geometric Langlands correspondence for SL(2, ℂ)
• Quantization of moduli spaces of flat connections and Liouville theory
• Lectures on the Langlands Program and Conformal Field Theory
• Quantisation conditions of the quantum Hitchin system and the real geometric Langlands correspondence
• Quantum Langlands duality and conformal field theory