Fixed point actions from convolutional neural networks
- URL: http://arxiv.org/abs/2311.17816v1
- Date: Wed, 29 Nov 2023 17:10:49 GMT
- Title: Fixed point actions from convolutional neural networks
- Authors: Kieran Holland, Andreas Ipp, David I. M\"uller, Urs Wenger
- Abstract summary: Lattice gauge-equivariant convolutional neural networks (L-CNNs) can be used to form arbitrarily shaped Wilson loops.
We use L-CNNs to describe fixed point (FP) actions which are based on renormalization group transformations.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Lattice gauge-equivariant convolutional neural networks (L-CNNs) can be used
to form arbitrarily shaped Wilson loops and can approximate any gauge-covariant
or gauge-invariant function on the lattice. Here we use L-CNNs to describe
fixed point (FP) actions which are based on renormalization group
transformations. FP actions are classically perfect, i.e., they have no lattice
artifacts on classical gauge-field configurations satisfying the equations of
motion, and therefore possess scale invariant instanton solutions. FP actions
are tree-level Symanzik-improved to all orders in the lattice spacing and can
produce physical predictions with very small lattice artifacts even on coarse
lattices. We find that L-CNNs are much more accurate at parametrizing the FP
action compared to older approaches. They may therefore provide a way to
circumvent critical slowing down and topological freezing towards the continuum
limit.
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