Translation- and gauge-equivariant neural networks (L-CNNs) predict Wilson loops, topological charge, and flux observables with orders-of-magnitude lower error than symmetry-breaking baselines, and neural gradient flow is proposed as a generative method for gauge configurations.
Improved Hamiltonian for Minkowski Yang-Mills Theory
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abstract
I develop an improved Hamiltonian for classical, Minkowski Yang-Mills theory, which evolves infrared fields with corrections from lattice spacing $a$ beginning at $O(a^4)$. I use it to investigate the response of Chern-Simons number to a chemical potential, and to compute the maximal Lyapunov exponent. Both quantities have small $a$ limits, in both cases within $10\% $ of the limit found using the unimproved (Kogut Susskind) Hamiltonian. For the maximal Lyapunov exponent the limits differ by about $5 \% $, significant at about $5 \sigma$, indicating that while a small $a$ limit exists, its value is corrupted by lattice artefacts. For the response of Chern-Simons number the statistics are not good enough to resolve $ 5 \% $ differences, but it seems possible in analogy with the Lyapunov exponent that the final answer depends on the lattice regulation.
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Symmetry-preserving neural networks in lattice field theories
Translation- and gauge-equivariant neural networks (L-CNNs) predict Wilson loops, topological charge, and flux observables with orders-of-magnitude lower error than symmetry-breaking baselines, and neural gradient flow is proposed as a generative method for gauge configurations.