2016/06/30 by Loriano Bonora, L. Bonora, A. A. Bytsenko +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Conjecture #Connection (principal bundle) #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic function #Invariant (physics) #Partition function (quantum field theory) #Quantum #Quantum field theory #Representation theory #Symmetry group #Topological quantum field theory #hep-th
paper · pdf · doi:10.1140/epjc/s10052-016-4468-z
19 pages
openalex created_date 2016/06/24 · arxiv created 2016/10/14 · openalex publication_date 2016/11/01 · arxiv updated 2016/12/21 · openalex updated_date 2026/08/05
We derive formulas for the classical Chern–Simons invariant of irreducible SU ( n )-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern–Simons invariant. On the basis of the Labastida–Mariño–Ooguri–Vafa conjecture we analyze a representation of the Chern–Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities.