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arXiv · 1606.02554

Chern-Simons Invariants on Hyperbolic Manifolds and Topological Quantum Field Theories

Loriano Bonora·Andrey A. Bytsenko·Antonio E. Goncalves
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Abstract

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 Labastida-Marino-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.

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Loriano Bonora, Andrey A. Bytsenko, Antonio E. Goncalves. 2016-10-14. Chern-Simons Invariants on Hyperbolic Manifolds and Topological Quantum Field Theories. https://doi.org/10.1140/epjc%2Fs10052-016-4468-z

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