Chern–Simons invariants on hyperbolic manifolds and topological quantum field theories

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• 作者：L. Bonora ; A. A. Bytsenko ; A. E. Gonçalves
• 刊名：The European Physical Journal C - Particles and Fields
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：76
• 期：11
• 全文大小：560 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Elementary Particles and Quantum Field Theory
  Nuclear Physics, Heavy Ions and Hadrons
  Physics beyond the Standard Model
  Measurement Science and Instrumentation
  Astronomy, Astrophysics and Cosmology
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1434-6052
• 卷排序：76

文摘

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.