Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-02-16
Class.Quant.Grav.23:3895-3916,2006
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, no figures, LATEX. To appear in the Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/23/11/014
The purpose of this paper is to provide the reader with a collection of results which can be found in the mathematical literature and to apply them to hyperbolic spaces that may have a role in physical theories. Specifically we apply K-theory methods for the calculation of brane charges and RR-fields on hyperbolic spaces (and orbifolds thereof). It is known that by tensoring K-groups with the rationals, K-theory can be mapped to rational cohomology by means of the Chern character isomorphisms. The Chern character allows one to relate the analytic Dirac index with a topological index, which can be expressed in terms of cohomological characteristic classes. We obtain explicit formulas for Chern character, spectral invariants, and the index of a twisted Dirac operator associated with real hyperbolic spaces. Some notes for a bivariant version of topological K-theory (KK-theory) with its connection to the index of the twisted Dirac operator and twisted cohomology of hyperbolic spaces are given. Finally we concentrate on lower K-groups useful for description of torsion charges.
Bonora Loriano
Bytsenko Andrei
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