Abstract
The neural ordinary differential equation (neural ODE) is a novel machine learning architecture whose weights are smooth functions of the continuous depth. We apply the neural ODE to holographic QCD by regarding the weight functions as a bulk metric, and train the machine with lattice QCD data of chiral condensate at finite temperature. The machine finds consistent bulk geometry at various values of temperature and discovers the emergent black hole horizon in the holographic bulk automatically. The holographic Wilson loops calculated with the emergent machine-learned bulk spacetime have consistent temperature dependence of confinement and Debye-screening behavior. In machine learning models with physically interpretable weights, the neural ODE frees us from discretization artifact leading to difficult ingenuity of hyperparameters, and improves numerical accuracy to make the model more trustworthy.
Highlights
The anti-de Sitter / deep learning (AdS/DL) correspondence takes a different approach[4, 5, 8, 10] by implementing the holographic principle[11–13] in a deep neural network, where the neural network is regarded as the classical equation of motion for propagating fields on a discretized curved spacetime
We applied the Neural ODE to the AdS/DL correspondence, where the emergent spacetime in the gravity side of the AdS/CFT correspondence is regarded as a deep neural network
Since the classical spacetime is continuous and smooth, the weights of the network need to be interpreted as a smooth function of the depth, the Neural ODE provides a very natural scheme for training the bulk geometry
Summary
Applying machine learning to solve physics problems[1, 2] has generated a growing research interest in recent years. Further progress has been made by the neural network renormalization group (Neural RG)[7], which learns to construct the exact holographic mapping between the boundary and the bulk field theories at the partition function level. The temperature dependence of holographic Wilson loops, calculated by the emergent geometry trained with the Neural ODE, turns out to coincide qualitatively with the known lattice QCD results of the Wilson loops. IV, we introduce a way to calculate consistent full components of the metric from the emergent volume factor, with which we calculate holographic Wilson loops They qualitatively agree with Wilson loops evaluated in lattice QCD.
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