Curvature dependence of running gauge coupling and confinement in AdS-CFT correspondence

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