Hyperbolic Space Forms and Orbifold Compactification in M-Theory

Abstract

We analyze solutions of supergravity and string theories which involve real hyperbolic spaces. Examples of string compactifications are given in terms of hyperbolic coset spaces of finite volume Γ\HN , where Γ is a discrete group of isometries of HN . We describe finite flux and the tensor kernel associated with hyperbolic spaces. The special case of an 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.