Conformal Fields from Neural Networks
This work addresses the challenge of modeling conformal field theories using neural networks, offering a novel computational framework for physicists studying quantum field theories, though it appears incremental as it builds on existing embedding formalism and neural network techniques.
The paper tackles the problem of constructing conformal fields in D dimensions by using Lorentz-invariant ensembles of homogeneous neural networks in higher dimensions, computing exact four-point correlators and performing conformal block decompositions to analyze spectra. It results in constructing generalized free CFTs, such as the free boson, through the infinite-width Gaussian process limit of neural networks, with extensions to deep networks providing recursion relations for conformal dimensions and four-point functions.
We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be computed using the parameter space description of the neural network. Exact four-point correlators are computed in a number of examples, and we perform a 4D conformal block decomposition that elucidates the spectrum. In some examples the analysis is facilitated by recent approaches to Feynman integrals. Generalized free CFTs are constructed using the infinite-width Gaussian process limit of the neural network, enabling a realization of the free boson. The extension to deep networks constructs conformal fields at each subsequent layer, with recursion relations relating their conformal dimensions and four-point functions. Numerical approaches are discussed.