标题： 自举SU(3)格点杨-米尔斯理论 显示英文标题

标题： Bootstrapping SU(3) Lattice Yang-Mills Theory

摘要： 我们应用正性自举方法到SU(3)格点杨-米尔斯(YM)理论，通过引入多迹威尔逊环算符，扩展了之前对大N和SU(2)理论的研究。 利用厄米特性和反射正性条件，以及施温格-戴森(SD)环方程，我们计算了二维、三维和四维YM理论中平面威尔逊环期望值的严格界限。 我们的结果表现出明显的收敛性，并与已知的解析或数值结果一致。 为了增强该方法，我们引入了一种新颖的扭转-反射正性条件，我们证明该条件在二维YM理论中是精确的。 此外，我们提出了一种维度缩减截断，其中威尔逊环算符被有效限制在一个低维子平面上，大大简化了计算。 双迹威尔逊环的SD方程也得到了详细推导。 我们的发现表明，正性自举方法广泛适用于单迹情况以外的高秩规范理论，为使用基于正性的方法进一步研究规范理论提供了坚实的基础。 显示英文摘要

摘要： We apply the positivity bootstrap approach to SU(3) lattice Yang-Mills (YM) theory, extending previous studies of large N and SU(2) theories by incorporating multiple-trace Wilson loop operators. Utilizing Hermitian and reflection positivity conditions, along with Schwinger-Dyson (SD) loop equations, we compute rigorous bounds for the expectation values of plaquette Wilson loop in 2D, 3D, and 4D YM theories. Our results exhibit clear convergence and are consistent with known analytic or numerical results. To enhance the approach, we introduce a novel twist-reflection positivity condition, which we prove to be exact in the 2D YM theory. Additionally, we propose a dimensional-reduction truncation, where Wilson loop operators are effectively restricted to a lower-dimensional subplane, significantly simplifying the computations. SD equations for double-trace Wilson loops are also derived in detail. Our findings suggest that the positivity bootstrap method is broadly applicable to higher-rank gauge theories beyond the single-trace cases, providing a solid foundation for further non-perturbative investigations of gauge theories using positivity-based methods.