标题： 诱导QCD II：数值结果 显示英文标题

标题： Induced QCD II: Numerical results

摘要： 我们用数值方法研究了连续 $\text{SU}(N_c)$ 非阿贝尔规范场理论在欧几里得时空晶格上的另一种离散化方法，该方法最初由 Budzcies 和 Zirnbauer 对于规范群 $\text{U}(N_c)$ 提出。 这种离散化可以被重新表述，使得规范场的自相互作用是由对 $N_b$ 个辅助玻色子场的路径积分诱导的，这些辅助场以线性方式耦合到规范场。 在本系列的第一篇论文中，我们已经证明了如果$N_b$大于$N_c-\frac{3}{4}$，则该理论在$d=2$维度下重现连续的$\text{SU}(N_c)$麦克斯韦理论，并且按照 Budzcies 和 Zirnbauer 的论证，我们推测这一结论对于$d>2$依然成立。 在本文中，我们通过进行最简单的非平凡情况下的格点模拟来检验这一推测，即三维中的规范群$\text{SU}(2)$。 我们展示了由诱导理论计算出的可观测量，例如静态$q\bar q$势和去禁闭相变温度，与由普通回路作用计算出的相同可观测量一致，误差仅限于格点效应。 我们还发现，$N_b$的界可以放松到$N_c-\frac{5}{4}$，正如我们在之前论文中所猜测的那样。 关于如何利用新的离散化来改变路径积分中的积分顺序以得到 QCD 的对偶表述的研究留待将来完成。 显示英文摘要

摘要： We numerically explore an alternative discretization of continuum $\text{SU}(N_c)$ Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer for gauge group $\text{U}(N_c)$. This discretization can be reformulated such that the self-interactions of the gauge field are induced by a path integral over $N_b$ auxiliary bosonic fields, which couple linearly to the gauge field. In the first paper of the series we have shown that the theory reproduces continuum $\text{SU}(N_c)$ Yang-Mills theory in $d=2$ dimensions if $N_b$ is larger than $N_c-\frac{3}{4}$ and conjectured, following the argument of Budzcies and Zirnbauer, that this remains true for $d>2$. In the present paper, we test this conjecture by performing lattice simulations of the simplest nontrivial case, i.e., gauge group $\text{SU}(2)$ in three dimensions. We show that observables computed in the induced theory, such as the static $q\bar q$ potential and the deconfinement transition temperature, agree with the same observables computed from the ordinary plaquette action up to lattice artifacts. We also find that the bound for $N_b$ can be relaxed to $N_c-\frac{5}{4}$ as conjectured in our earlier paper. Studies of how the new discretization can be used to change the order of integration in the path integral to arrive at dual formulations of QCD are left for future work.