Stratified fiber bundles, Quinn homology and brane stability of hyperbolic orbifolds

Andrey A. Bytsenko, Richard J. Szabo, Anca Tureanu

Research output: Contribution to journalArticle

Abstract

We revisit the problem of stability of string vacua involving hyperbolic orbifolds using methods from homotopy theory and K-homology. 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 K-theory of their fundamental groups and Quinn homology to derive criteria for brane stability in terms of an Atiyah-Hirzebruch type spectral sequence with its lift to K-homology. Stable D-branes in this setting carry stratified charges which induce new additive structures on the corresponding K-homology groups. We extend these considerations to backgrounds which support H-flux, where we use K-groups of twisted group algebras of the fundamental groups to analyze stability of locally symmetric spaces with K-amenable isometry groups, and derive stability conditions for branes wrapping the fibers of an Eilenberg-MacLane spectrum functor.

Original languageEnglish
Article number165401
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number16
DOIs
Publication statusPublished - 14 Mar 2016

Keywords

  • criteria for brane stability
  • homotopy theory
  • hyperbolic orbifolds
  • Quinn homology

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

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