Curvature dependence of running gauge coupling and confinement in AdS-CFT correspondence - art. no. 044014

We construct a type IIB supergravity (viewed as dilatonic gravity) backgrou nd with a nontrivial dilaton and with curved four-dimensional space. Such a background may describe another vacuum of maximally supersymmetric Yang-Mi lls theory or strong coupling regime of (non)supersymmetric gauge theory wi th (powerlike) running gauge coupling which depends on curvature. A curvatu re dependent quark-antiquark potential is calculated when the geometry type of hyperbolic (or de Sitter universe) shows (or does not show) the tendenc y of the confinement. A generalization of the type IIB supergravity backgro und with a nonconstant axion is presented. The quark-antiquark potential, b eing again curvature dependent, has the possibility to produce the standard area law for large separations.