Discrete Liouville equation and Teichmüller theory

Abstract

The relationship (both classical and quantum mechanical) between the discrete Liouville equation and Teichmüller theory is reviewed.

24 pages, 11 figures, submitted to Handbook in Teichmüller theory, minor corrections, references added

References in corpus (8)

• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Liouville Field Theory -- A decade after the revolution
• Discrete Heisenberg-Weyl Group and Modular Group
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
• Noncommutative Hypergeometry
• Liouville Theory: Quantum Geometry of Riemann Surfaces
• Discrete evolution for the zero-modes of the Quantum Liouville Model

Cited by in corpus (3)

• Classical and Quantum Dilogarithm Identities
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• Angular Momentum and Gravimagnetization of the $\mathcal{N}=2$ SYM vacuum