论文标题
$ 2+1 $ d QCD的理论中的限制和伪级粘合球谱。
Confinement and Pseudoscalar Glueball Spectrum in the $2+1$D QCD-Like Theory from the Non-Susy D$2$ Brane
论文作者
论文摘要
在这里，我们使用全息方法研究了$ 2+1 $ dimensional QCD的两个重要特性 - 限制和伪粘合球谱。我们认为各向同性非愉快的d $ 2 $ brane的低能解耦几何形状。我们发现相应的量规理论与$ 2+1 $ -DIM YANG-MILLS理论具有$λ^2 $。在极端极限（即BPS极限）下，该规程理论还原为超级理论。从测试字符串的Nambu-Goto动作中，计算了位于边界上的\ qq对的电势。在总体\ qq分离下，它给出了QCD通量管的张力$σ$。 $σ$的参数依赖项如图所示。发现$σ$是有效耦合$λ^2 $的单调增加的功能。相比之下，发现$ \sqrtσ/g_ \ text {ym}^2n_c $与先前的结果完全匹配。在下一部分中，我们考虑在上述重力背景中轴突场的波动。从波动的线性化场方程中，我们使用WKB近似计算$ 0^{ - +} $的质谱。发现伪级质量与字符串张力大约为$ m_ {0^{ - +}}/\sqrtσ\ of前三个能量状态，$ n = 0，\，\，1，\，2 $。
Here we study two important properties of $2+1$ dimensional QCD -- confinement and pseudoscalar glueball spectrum -- with holographic approach. We consider the low energy decoupled geometry of the isotropic non-susy D$2$ brane. We find the corresponding gauge theory is similar to the $2+1$-dim Yang-Mills theory with the running coupling $λ^2$. At the extremal limit (i.e. BPS limit), this gauge theory reduces to the super-YM theory. From the Nambu-Goto action of a test string, the potential of a \qq pair located on the boundary is calculated. At large \qq separation it gives the tension $σ$ of the QCD flux-tube. The parametric dependencies of $σ$ is shown pictorially. It is found that $σ$ is a monotonically increasing function of the effective coupling $λ^2$. In comparison, $\sqrtσ/g_\text{YM}^2N_c$ is found to match accurately with the previous results. In the next part, we consider fluctuation of the axion field in the aforementioned gravity background. From the linearized field equation of the fluctuation we calculate the mass spectrum of $0^{-+}$ numerically using the WKB approximation. The pseudoscalar mass is found to be related to the string tension approximately as $M_{0^{-+}}/\sqrtσ\approx 3(n+2)$ for first three energy states, $n=0,\,1,\,2$.
