Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
arXiv:hep-th/0006156 · doi:10.1007/s002200100412
Abstract
The quantum discrete Liouville model in the strongly coupled regime, 1<c<25, is formulated as a well defined quantum mechanical problem with unitary evolution operator. The theory is self-dual: there are two exponential fields related by Hermitean conjugation, satisfying two discrete quantum Liouville equations, and living in mutually commuting subalgebras of the quantum algebra of observables.
Latex2e, 20 pages
References in corpus (1)
Cited by in corpus (106)
- Dilaton Gravity in Two Dimensions
- The quantum dilogarithm and representations quantum cluster varieties
- Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
- SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
- Essays on the theory of elliptic hypergeometric functions
- Baxter Q-Operators and Representations of Yangians
- Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
- Seifert fibering operators in 3d theories
- Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
- Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
- Braids, Walls, and Mirrors
- On CFT and Quantum Chaos
- Matrix models from operators and topological strings
- R-operator, co-product and Haar-measure for the modular double of U_q(sl(2,R))
- High-temperature asymptotics of supersymmetric partition functions
- On the spectrum of Dehn twists in quantum Teichmuller theory
- Lie symmetries of multidimensional difference equations
- Higher-Level Appell Functions, Modular Transformations, and Characters
- S^3/Z_n partition function and dualities
- Classical and Quantum Dilogarithm Identities
- Three-dimensional supersymmetric gauge theories and partition functions on Seifert manifolds: A review
- Quivers, YBE and 3-manifolds
- High-Temperature Expansion of Supersymmetric Partition Functions
- An analog of a modular functor from quantized Teichm"uller theory
- Exact solution of the Faddeev-Volkov model
- Unit circle elliptic beta integrals
- Yang-Baxter Maps, Discrete Integrable Equations and Quantum Groups
- The star-triangle relation, lens partition function, and hypergeometric sum/integrals
- Noncommutative integrability, paths and quasi-determinants
- Hyperbolic Structure Arising from a Knot Invariant
- An exact renormalization formula for the Maryland model
- Quantum Riemann Surfaces in Chern-Simons Theory
- Complex Quantum Chern-Simons
- A new formulation of the Teichmüller TQFT
- Baxter operators with deformed symmetry
- On the fusion matrix of the N=1 Neveu-Schwarz blocks
- Hyperbolicity of Partition Function and Quantum Gravity
- 3d N=2 Theories from Cluster Algebras
- Elliptic beta integrals and solvable models of statistical mechanics
- A Q-operator for the twisted XXX model
- Discrete evolution for the zero-modes of the Quantum Liouville Model
- The pentagon relation and incidence geometry
- A Relativistic Conical Function and its Whittaker Limits
- Super-tetrahedra and super-algebras
- Liouville quantum gravity with matter central charge in : a probabilistic approach
- Thermodynamics and conformal properties of XXZ chains with alternating spins
- Quantum Teichmüller space from quantum plane
- Orthogonal Polynomials in Mathematical Physics
- From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation
- Scattering of Long Folded Strings and Mixed Correlators in the Two-Matrix Model
- Quantization of three-wave equations
- Fermi gas approach to general rank theories and quantum curves
- Theta series, wall-crossing and quantum dilogarithm identities
- Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group
- On the Volume Conjecture for hyperbolic Dehn-filled -manifolds along the figure-eight knot
- On -Whittaker functions
- Discrete Liouville equation and Teichmüller theory
- Theta functions, quantum tori and Heisenberg groups
- Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
- High-temperature asymptotics of the 4d superconformal index
- Liouville dynamical percolation
- On beta pentagon relations
- Long Strings and Chiral Non-Singlets in Matrix Quantum Mechanics
- Relative Reshetikhin-Turaev invariants, hyperbolic cone metrics and discrete Fourier transforms II
- The Quantum Gravity Disk: Discrete Current Algebra
- Discrete Fourier transforms, quantum -symbols and deeply truncated tetrahedra
- Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d theories
- Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
- The integrable structure of nonrational conformal field theory
- Classical elliptic hypergeometric functions and their applications
- The R-operator for Modular Double
- Volkov's Pentagon for the Modular Quantum Dilogarithm
- A relative version of the Turaev-Viro invariants and the volume of hyperbolic polyhedral 3-manifolds
- Phase constants in the Fock-Goncharov quantum cluster varieties
- Topological Aspects of Matters and Langlands Program
- Continuum limit of the Volterra model, separation of variables and non standard realizations of the Virasoro Poisson bracket
- The solution of the quantum T-system for arbitrary boundary
- On Bailey pairs for supersymmetric gauge theories on
- Chiral Potts model and the discrete Sine-Gordon model at roots of unity
- Asymptotics of some quantum invariants of the Whitehead chains
- On modular double of semisimple quantum groups
- Heisenberg double and Drinfeld double of the quantum superplane
- 3D-3D Correspondence from Seifert Fibering Operators
- Phase constants in the Fock-Goncharov quantization of cluster varieties: long version
- Computation of leading coefficients in asymptotics of relative quantum invariants
- Three-dimensional quantum gravity from the quantum pseudo-Kähler plane
- Quantizing the discrete Painlevé VI equation : The Lax formalism
- Complex rational Ruijsenaars model. The two-particle case
- A series of spectral gaps for the almost Mathieu operator with a small coupling constant
- Generalized Cherednik-Macdonald identities
- Baxterization of GL_q(2) and its application to the Liouville model and some other models on a lattice
- On the difference equations with periodic coefficients
- A quantization of moduli spaces of 3-dimensional gravity
- Quantum Trilogy: Discrete Toda, Y-System and Chaos
- Black Hole Entropy and the Pseudo Goldstone Bosons of Conformal Symmetry
- Irreducible self-adjoint representations of quantum Teichmüller space and the phase constants
- Volume conjecture, geometric decomposition and deformation of hyperbolic structures
- On explicit realization of algebra of complex divided powers of
- Braiding Operator via Quantum Cluster Algebra
- On explicit realization of algebra of complex powers of generators of
- Nonperturbative refined topological string
- Evolution operators for quantum chains
- Anomalies and Holomorphy in Supersymmetric Chern-Simons-Matter Theories
- Cluster Partition Function and Invariants of 3-manifolds
- On the asymptotic expansion for the relative Reshetikhin-Turaev invariants of fundamental shadow link pairs
- Notes on holonomy matrices of hyperbolic 3-manifolds with cusps