On the spectrum of Dehn twists in quantum Teichmuller theory

Abstract

The operator realizing a Dehn twist in quantum Teichmuller theory is diagonalized and continuous spectrum is obtained. This result is in agreement with the expected spectrum of conformal weights in quantum Liouville theory at c>1. The completeness condition of the eigenvectors includes the integration measure which appeared in the representation theoretic approach to quantum Liouville theory by Ponsot and Teschner. The underlying quantum group structure is also revealed.

13 pages,8 figures,LaTeX2e

References in corpus (4)

• Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• Tensor Products of Principal Unitary Representations of Quantum Lorentz Group and Askey-Wilson Polynomials
• The colored Jones polynomials and the simplicial volume of a knot

Cited by in corpus (35)

• Conformal Bootstrap, Universality and Gravitational Scattering
• Noncommutative Hypergeometry
• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Operators from mirror curves and the quantum dilogarithm
• On the relation between quantum Liouville theory and the quantized Teichm"uller spaces
• 3D Gravity, Point Particles and Liouville Theory
• Yang-Baxter Maps, Discrete Integrable Equations and Quantum Groups
• Quantum Riemann Surfaces in Chern-Simons Theory
• On Quantizing Teichmüller and Thurston theories
• Painlevé monodromy manifolds, decorated character varieties and cluster algebras
• Braids, Complex Volume, and Cluster Algebra
• Teichmüller Theory of Bordered Surfaces
• Quantum Teichmüller space from quantum plane
• The dilogarithmic central extension of the Ptolemy-Thompson group via the Kashaev quantization
• Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group
• Orbifold Riemann surfaces and geodesic algebras
• Quantum Teichmüller space and Kashaev algebra
• Lecture Notes on Quantum Teichmuller Theory
• Pentagon identities arising in supersymmetric gauge theory computations
• Ratio coordinates for higher Teichmüller spaces
• SU(2)/SL(2) knot invariants and KS monodromies
• Factorization Rules in Quantum Teichmüller Theory
• Three-dimensional quantum gravity from the quantum pseudo-Kähler plane
• Representations of a quantum-deformed Lorentz algebra, Clebsch-Gordan map, and Fenchel-Nielsen representation of complex Chern-Simons theory at level-$N$
• Asymptotic aspects of the Teichmüller TQFT
• Finite dimensional quantum Teichmüller space from the quantum torus at root of unity
• Irreducible self-adjoint representations of quantum Teichmüller space and the phase constants
• Braiding Operator via Quantum Cluster Algebra
• Modular functors with infinite dimensional Hilbert spaces
• On explicit realization of algebra of complex powers of generators of $U_q(\mathfrak{sl}(3))$
• Weyl asymptotics for functional difference operators with power to quadratic exponential potential
• Extension of geodesic algebras to continuous genus
• Painlevé Kernels and Surface Defects at Strong Coupling
• Relativistic Kinematics of Two-Parametric Riemann Surface in Genus Two