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-supersymmetric D2 brane. We find the corresponding gauge theory is similar to the $2+1$-dimensional Yang-Mills (YM) theory with the running coupling ${\lambda }^2$. At the extremal limit (i.e., Bogomol’nyi-Prasad-Sommerfield limit), this gauge theory reduces to the super-YM theory. From the Nambu-Goto action of a test string, the potential of a $Q\text{−}\overline{Q}$ pair located on the boundary is calculated. At large $Q\text{−}\overline{Q}$ separation, it gives the tension $\sigma$ of the QCD flux tube. The parametric dependence of $\sigma$ is shown pictorially. It is found that $\sigma$ is a monotonically increasing function of the effective coupling ${\lambda }^2$. In comparison, $\sqrt{\sigma }/g_{\mathrm{YM}}^2{N}_c$ 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 Wentzel-Kramers-Brillouin approximation. The pseudoscalar mass is found to be related to the string tension approximately as $M_{0^{-+}}/\sqrt{\sigma }\approx 3(n+2)$ for first three energy states, $n=0$, 1, 2.

中文翻译：

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非SUSYD2分子在类2 + 1DQCD理论中的约束和拟标量胶球谱

在这里，我们研究了两个重要的特性 $\mathrm{2个}+\mathrm{1个}$全息方法的三维QCD（约束和伪标量胶球光谱）。我们考虑了各向同性非超对称D2油膜的低能量解耦几何形状。我们发现相应的量规理论类似于$\mathrm{2个}+\mathrm{1个}$运转耦合的三维杨-米尔斯（YM）理论 ${\lambda }^{\mathrm{2个}}$。在极值极限（即Bogomol'nyi-Prasad-Sommerfield极限）处，该规范理论简化为超级YM理论。根据测试字符串的Nambu-Goto动作，$问\text{-}\overline{问}$计算位于边界上的一对。大体上$问\text{-}\overline{问}$ 分离，它给张力 $\sigma$QCD助焊剂管的 的参数依赖性$\sigma$如图所示。发现$\sigma$ 是有效耦合的单调递增函数 ${\lambda }^{\mathrm{2个}}$。相比下，$\sqrt{\sigma }/G_M^{\mathrm{2个}}{ñ}_C$被发现与先前的结果准确匹配。在下一部分中，我们将考虑上述重力背景下的轴场波动。从波动的线性场方程，我们可以计算出$0^{-+}$使用Wentzel-Kramers-Brillouin近似数值。发现伪标量质量大约与弦张力有关。${\mathrm{中号}}_{0^{-+}}/\sqrt{\sigma }\approx 3（ñ+\mathrm{2个}）$ 对于前三个能量状态 $ñ=0$，1、2