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 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.

翻译：不动点格点作用量被设计为在经典层面上具有不受离散化效应影响的连续性质，并在量子层面上减少格点赝象。它们提供了利用较粗糙格点提取连续物理的可能性，从而有助于规避临界慢化以及向连续极限逼近时的拓扑冻结问题。实际应用的关键要素在于找到不动点作用量的精确且紧凑的参数化形式，因为其许多性质仅通过隐式定义。本文采用机器学习方法重新审视如何参数化不动点作用量的问题。特别地，我们利用具有严格规范不变性的卷积神经网络，获得了四维SU(3)规范理论的不动点作用量。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，这是未来蒙特卡洛模拟的必要初步步骤。