Solution of the 5D Einstein equations in a dilaton background model

TL;DR

This paper derives explicit solutions to 5D Einstein equations with a dilaton field, demonstrating how these solutions can model confinement, meson trajectories, and asymptotic freedom in a holographic QCD framework.

Contribution

It provides a unique method to determine the dilaton and its potential from metric ansatzes, linking gravitational backgrounds to QCD phenomena.

Findings

Confinement arises naturally from the metric and dilaton solutions.

Meson Regge trajectories constrain the background fields.

The model can incorporate asymptotic freedom.

Abstract

We obtain an explicit solution of the 5d Einstein equations in a dilaton background model. We demonstrate that for each metric ansatz that only depends on the extra coordinate, it is possible to uniquely determine the dilaton field and its potential consistently with the 5d Einstein equation. In this holographic dual model of QCD, conformal symmetry of the Anti-de-Sitter metric near the 4d boundary is broken by a term that leads to an area law for the Wilson loop. We verify that confinement of the string modes dual to mesons follows from the metric background and the corresponding dilaton solution of the gravity-dilaton coupled equations. In addition, we show that the meson Regge trajectories constrain the metric and corresponding dilaton background within the area law requirement. We can also incorporate asymptotic freedom in the gravity background within the model.