Stratified fiber bundles, Quinn homology and brane stability of hyperbolic orbifolds
Abstract
We revisit the problem of stability of string vacua involving hyperbolic orbifolds using methods from homotopy theory and Khomology. We propose a definition of Type II string theory on such backgrounds that further carry stratified systems of fiber bundles, which generalize the more conventional orbifold and symmetric string backgrounds, together with a classification of wrapped branes by a suitable generalized homology theory. For spaces stratified fibered over hyperbolic orbifolds we use the algebraic Ktheory of their fundamental groups and Quinn homology to derive criteria for brane stability in terms of an AtiyahHirzebruch type spectral sequence with its lift to Khomology. Stable Dbranes in this setting carry stratified charges which induce new additive structures on the corresponding Khomology groups. We extend these considerations to backgrounds which support Hflux, where we use Kgroups of twisted group algebras of the fundamental groups to analyze stability of locally symmetric spaces with Kamenable isometry groups, and derive stability conditions for branes wrapping the fibers of an EilenbergMacLane spectrum functor.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 April 2016
 DOI:
 10.1088/17518113/49/16/165401
 arXiv:
 arXiv:1502.07560
 Bibcode:
 2016JPhA...49p5401B
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Algebraic Topology;
 Mathematics  KTheory and Homology
 EPrint:
 29 pages