5 research outputs found
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