Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network
This work addresses a bottleneck in lattice quantum field theory simulations for physicists, offering an incremental improvement in action parametrization.
The authors tackled the problem of parametrizing fixed point actions for SU(3) gauge theory to reduce lattice artifacts and enable efficient Monte Carlo simulations, achieving superior parametrizations compared to prior work using gauge equivariant convolutional neural networks.
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.