Curvature Dependence of Running Gauge Coupling and Confinement in AdS/CFT Correspondence

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Abstract
We construct IIB supergravity (viewed as dilatonic gravity) background with non-trivial dilaton and with curved four-dimensional space. Such background describes the strong coupling regime of non-SUSY gauge theory with (power-like) running gauge coupling which depends on curvature. We also speculate on such running as caused by ``AdS time''. Curvature dependent quark-antiquark potential is calculated where geometry type (de Sitter or hyperbolic) predicts (or not) the confinement. Generalization of such background (SUSY or non-SUSY) with non-constant axion is presented. Quark-antiquark potential being again curvature-dependent may produce the standard area law for large separations. It is interesting that de Sitter Universe with axion supports the confinement.

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