Quantum Dilogarithm

Abstract

A quantum generalization of Rogers' five term, or ``pentagon'' dilogarithm identity is suggested. It is shown that the classical limit gives usual Rogers' identity. The case where the quantum identity is realized in finite dimensional space is also considered and the quantum dilogarithm is constructed as a function on Fermat curve, while the identity itself is equivalent to the restricted star-triangle relation introduced by Bazhanov and Baxter.

9 pages

Cited by in corpus (183)

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• Permeable conformal walls and holography
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• A lecture on the Liouville vertex operators
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• Braids, Walls, and Mirrors
• Seiberg-Witten theory as a Fermi gas
• Real Multiplication and noncommutative geometry
• Operators from mirror curves and the quantum dilogarithm
• Matrix models from operators and topological strings
• R-operator, co-product and Haar-measure for the modular double of U_q(sl(2,R))
• The hyperbolic volume of knots from quantum dilogarithm
• Higher-Level Appell Functions, Modular Transformations, and Characters
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models
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• Semiclassical Analysis of the 3d/3d Relation
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• Aspects of Defects in 3d-3d Correspondence
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• S-duality as a beta-deformed Fourier transform
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• Positive Representations of Split Real Simply-laced Quantum Groups
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• Baxter operators with deformed symmetry
• The universal Racah-Wigner symbol for Uq(osp(1|2))
• A new pentagon identity for the tetrahedron index
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• Exponential Networks, WKB and Topological String
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• 3d N=2 Theories from Cluster Algebras
• Hyperbolicity of Partition Function and Quantum Gravity
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• 3D symplectic map
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• D-Brane Amplitudes in Topological String on Conifold
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• Orthogonal Polynomials in Mathematical Physics
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• Exact quantum S-matrices for solitons in simply-laced affine Toda field theories
• Fermi gas approach to general rank theories and quantum curves
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• Motivic correlators, cluster varieties and Zagier's conjecture on zeta(F,4)
• Modified melting crystal model and Ablowitz-Ladik hierarchy
• Scattering diagrams, theta functions, and refined tropical curve counts
• Infrared phases of 3D Class R theories
• Explicit Free Parameterization of the Modified Tetrahedron Equation
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
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• Comments on Exchange Graphs in Cluster Algebras
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• The Yang-Baxter relation and gauge invariance
• The Lerch zeta function III. Polylogarithms and special values
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• Multispecies Weighted Hurwitz Numbers
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• Problems on invariants of knots and 3-manifolds
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• Dilogarithm identities in cluster scattering diagrams
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• Restricted Quantum Theory of Affine Toda Solitons
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• On the Fermionic Quasi-particle Interpretation in Minimal Models of Conformal Field Theory
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• An Elliptic Parameterisation of the Zamolodchikov Model
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• The Virasoro fusion kernel and Ruijsenaars' hypergeometric function
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• Heisenberg double and Drinfeld double of the quantum superplane
• The Graphs of Quantum Dilogarithm
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• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• Three-dimensional quantum gravity from the quantum pseudo-Kähler plane
• Asymptotic aspects of the Teichmüller TQFT
• Quantum Field Theory and the Volume Conjecture
• Baxterization of GL_q(2) and its application to the Liouville model and some other models on a lattice
• Quantum dilogarithm identities for n-cycle quivers
• The embedding structure and the shift operator of the U(1) lattice current algebra
• A quantization of moduli spaces of 3-dimensional gravity
• Interpolating factorizations for acyclic Donaldson--Thomas invariants
• The geometry of cluster varieties from surfaces
• QHI Theory, I: 3-Manifolds Scissors Congruence Classes and Quantum Hyperbolic Invariants
• Heisenberg-Euler and the Quantum Dilogarithm
• Finite dimensional quantum Teichmüller space from the quantum torus at root of unity
• Quantum Trilogy: Discrete Toda, Y-System and Chaos
• Braiding Operator via Quantum Cluster Algebra
• Quantum dilogarithms and partition q-series
• Irreducible self-adjoint representations of quantum Teichmüller space and the phase constants
• Modular resurgence, $q$-Pochhammer symbols, and quantum operators from mirror curves
• Quantum computation and real multiplication
• A family of structure isomorphisms for the Cohomological Hall Algebra of an acyclic quiver
• Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations
• Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariants