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

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 generalise 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 analyse 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.Comment: 29 page

Hyperbolic Space Forms and Orbifold Compactification

Abstract: We analyze solutions of string theory and supergravity which involve real hyperbolic spaces. Examples of string compactifications are given in terms of hyperbolic coset spaces of finite volume Γ\H N, where Γ is a discrete group of isometries of H N. We describe finite flux and the tensor kernel associated with hyperbolic spaces. The case of arithmetic geometry of Γ = SL(2, Z+iZ)/{±Id}, where Id is the identity matrix, is analyzed. We discuss supersymmetry surviving for supergravity solutions involving real hyperbolic space factors, string-supergravity correspondence and holography principle for a class of conformal field theories. – 1