介子背景模型下的5D爱因斯坦方程解
Solution of the 5D Einstein equations in a dilaton background model
摘要：
我们得到了在介子背景模型中的5d爱因斯坦方程的显式解。我们证明，对于每个仅取决于额外坐标的度规假设，可以唯一地确定与5d爱因斯坦方程一致的膨胀子场及其势。在这个QCD的全息对偶模型中，4d边界附近的Anti-de-Sitter度规的共形对称性被一个导致威尔逊圈面积律的项打破。我们验证了束缚的弦模式的介子对偶遵循的度规背景和相应的引力-介子耦合方程的介子解。此外，我们表明，介子Regge轨迹约束的度量和相应的介子的背景下的面积定律的要求。我们还可以在模型中加入重力背景中的渐近自由。
英文摘要：
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.
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