Fixed point lattice actions are designed to have continuum classical properties unaffected by discretization effects and reduced lattice artifacts at the quantum level. They provide a possible way to extract continuum physics with coarser lattices, thereby allowing one to circumvent problems with critical slowing down and topological freezing toward the continuum limit. A crucial ingredient for practical applications is to find an accurate and compact parametrization of a fixed point action, since many of its properties are only implicitly defined. Here we use machine learning methods to revisit the question of how to parametrize fixed point actions. In particular, we obtain a fixed point action for four-dimensional SU(3) gauge theory using convolutional neural networks with exact gauge invariance. The large operator space allows us to find superior parametrizations compared to previous studies, a necessary first step for future Monte Carlo simulations and scaling studies.

翻译：固定点格点作用量的设计旨在使其连续经典性质不受离散化效应影响，并在量子层面减少格点伪影。这为在较粗格点上提取连续物理提供了一条可行途径，从而能够规避趋近连续极限时出现的临界减速与拓扑冻结问题。实际应用中的关键环节在于寻找固定点作用量的精确紧凑参数化表示，因为其诸多性质仅被隐式定义。本文采用机器学习方法重新探讨固定点作用量的参数化问题。具体而言，我们通过具有严格规范不变性的卷积神经网络，获得了四维SU(3)规范理论的固定点作用量。广阔的算子空间使我们能够找到优于以往研究的参数化方案，这为未来开展蒙特卡洛模拟与标度研究奠定了必要的初步基础。