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

TL;DR

This paper explores how curvature influences the running gauge coupling and confinement in gauge theories via a constructed IIB supergravity background with non-trivial dilaton and curved spacetime, revealing curvature-dependent confinement behavior.

Contribution

It introduces a new IIB supergravity background with non-trivial dilaton and curvature, analyzing its impact on gauge coupling and confinement, including a generalization with a non-constant axion.

Findings

Curvature affects the quark-antiquark potential and confinement tendencies.

The geometry type influences the confinement behavior, showing hyperbolic or de Sitter universe effects.

Potential for standard area law at large separations in curved backgrounds.

Abstract

We construct IIB supergravity (viewed as dilatonic gravity) background with non-trivial 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 (power-like) running gauge coupling which depends on curvature. Curvature dependent quark-antiquark potential is calculated where the geometry type of hyperbolic (or de Sitter universe) shows (or not) the tendency of the confinement. Generalization of IIB supergravity background with non-constant axion is presented. Quark-antiquark potential being again curvature-dependent has a possibility to produce the standard area law for large separations.