论文标题
lattice Yang-Mills理论的引导程序
Bootstrap for Lattice Yang-Mills theory
论文作者
论文摘要
我们通过数值引导方法研究了$ su（\ infty）$ lattice yang-mills理论$ d = 2,3,4 $。它结合了makeenko-migdal循环方程式，在最大循环长度上，截止$ l _ {\ mathrm {max}} $，以及威尔逊循环某些矩阵的积极条件。我们的算法灵感来自P. Anderson和M. Kruczenski的开创性论文，但它的效率明显更高，因为它考虑了晶格理论的对称性，并使用了放松程序，并根据我们先前在Matrix Bootstrap上的工作一致。因此，在各种耦合和尺寸下，我们在平均值上获得了严格的上限和下限。对于$ d = 4 $，在强耦合阶段，下边界的数据似乎与MC数据接近，而弱耦合阶段中的上限数据很好地再现了3环扰动理论。我们的结果表明，这种引导方法可以为迄今为止毫无争议的蒙特卡洛方法提供切实的替代方法。
We study the $SU(\infty)$ lattice Yang-Mills theory at the dimensions $D=2,3,4$ via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with a cut-off $L_{\mathrm{max}}$ on the maximal length of loops, and positivity conditions on certain matrices of Wilson loops. Our algorithm is inspired by the pioneering paper of P. Anderson and M. Kruczenski but it is significantly more efficient, as it takes into account the symmetries of the lattice theory and uses the relaxation procedure in line with our previous work on matrix bootstrap. We thus obtain rigorous upper and lower bounds on the plaquette average at various couplings and dimensions. For $D=4$, the lower bound data appear to be close to the MC data in the strong coupling phase and the upper bound data in the weak coupling phase reproduce well the 3-loop perturbation theory. Our results suggest that this bootstrap approach can provide a tangible alternative to the, so far uncontested, Monte Carlo approach.
