Hyperbolicity of Partition Function and Quantum Gravity

Abstract

We study a geometry of the partition function which is defined in terms of a solution of the five-term relation. It is shown that the 3-dimensional hyperbolic structure or Euclidean AdS_3 naturally arises in the classical limit of this invariant. We discuss that the oriented ideal tetrahedron can be assigned to the partition function of string.

16 pages, 4 figures

References in corpus (10)

• Large N Field Theories, String Theory and Gravity
• The Black Hole in Three Dimensional Space Time
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Geometry of the 2+1 Black Hole
• Discrete Heisenberg-Weyl Group and Modular Group
• Quantum Dilogarithm
• Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
• A Link Invariant from Quantum Dilogarithm
• Classical 6j-symbols and the tetrahedron
• Hyperbolic Structure Arising from a Knot Invariant

Cited by in corpus (10)

• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Aspects of Defects in 3d-3d Correspondence
• A new formulation of the Teichmüller TQFT
• The Hitchin-Witten Connection and Complex Quantum Chern-Simons Theory
• 6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
• The Yang-Baxter relation and gauge invariance
• A Geometric Quantisation view on the AJ-conjecture for the Teichmüller TQFT
• New Pentagon Identities Revisited
• Asymptotic aspects of the Teichmüller TQFT
• State integral models and the tetrahedron equation