Hyperbolic Space Forms and Orbifold Compactification

Abstract

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