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Fixed point lattice actions are designed to have continuum classicalproperties unaffected by discretization effects and reduced lattice artifactsat the quantum level. They provide a possible way to extract continuum physicswith coarser lattices, thereby allowing to circumvent problems with criticalslowing down and topological freezing toward the continuum limit. A crucialingredient for practical applications is to find an accurate and compactparametrization of a fixed point action, since many of its properties are onlyimplicitly defined. Here we use machine learning methods to revisit thequestion of how to parametrize fixed point actions. In particular, we obtain afixed point action for four-dimensional SU(3) gauge theory using convolutionalneural networks with exact gauge invariance. The large operator space allows usto find superior parametrizations compared to previous studies, a necessaryfirst step for future Monte Carlo simulations.

Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network