Ray-Singer torsion for a hyperbolic 3-manifold and asymptotics of Chern-Simons-Witten invariant

1997/04/30 by Andrei A. Bytsenko, Luciano Vanzo, Sergio Zerbini
Mathematics · Physics and Astronomy · #3-manifold #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Chern–Simons theory #Gauge theory #Geometric and Algebraic Topology #Invariant (physics) #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum mechanics #Riemann hypothesis #Selberg trace formula #Semiclassical physics #Torsion (gastropod) #hep-th

paper · pdf · doi:10.1016/s0550-3213(97)00566-x

published as Nucl.Phys. B505 (1997) 641-659 · Latex file, 15 pages. Some improvements, grammatical mistakes and typos corrected

arxiv created 1997/08/22 · openalex publication_date 1997/11/01 · arxiv updated 2019/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The Ray-Singer torsion for a compact smooth hyperbolic 3-dimensional manifold \cal H³ is expressed in terms of Selberg zeta-functions, making use of the associated Selberg trace formulae. Applications to the evaluation of the semiclassical asymptotics of the Witten's invariant for the Chern-Simons theory with gauge group SU(2) as well as to the sum over topologies in 3-dimensional quantum gravity are presented.

Citations

• Partition Function of a Quadratic Functional and Semiclassical Approximation for Witten's 3-Manifold Invariant
• The sum over topologies in three-dimensional Euclidean quantum gravity
• A largek asymptotics of Witten's invariant of Seifert manifolds
• Quantum field theory and the Jones polynomial
• 2 + 1 dimensional gravity as an exactly soluble system
• Zeta function regularization of path integrals in curved spacetime
• R-Torsion and the Laplacian on Riemannian manifolds
• Invariants of 3-manifolds via link polynomials and quantum groups
• Classical and quantum conformal field theory