Application of gauge equivariant convolutional neural networks to learning a fixed point action for SU(3) gauge theory

Lattice gauge theory is pivotal in understanding nuclear physics and the strong interaction of quarks and gluons from first principles, shedding light on phenomena such as confinement and asymptotic freedom, and providing quantitative understanding of masses and decay rates of mesons and baryons. Scaling up corresponding Monte Carlo simulations faces challenges such as critical slowing down and topological freezing. One proposed approach to address these challenges is through the use of fixed point lattice actions. These actions preserve continuum classical properties even after discretization, thereby reducing lattice artifacts at the quantum level, but they can only be defined implicitly. Here, we employ machine learning, specifically lattice gauge equivariant convolutional neural networks (L-CNNs), to learn fixed point actions in a gauge symmetry preserving way. We obtain a fixed point action for four-dimensional SU(3) gauge theory which is superior to previous hand-crafted parametrizations. This advancement is crucial for future Monte Carlo simulations.