Year: 2019
Type: article
Abstract: We provide a deep Boltzmann machine (DBM) for the $\mathrm{AdS}/\mathrm{CFT}$ correspondence. Under the philosophy that the bulk spacetime is a neural network, we give a dictionary between those, and obtain a restricted DBM as a discretized bulk scalar field theory in curved geometries. The probability distribution as training data is the generating functional of the boundary quantum field theory, and it trains neural network weights which are the metric of the bulk geometry. The deepest layer implements black hole horizons, and an employed regularization for the weights is an Einstein action. A large ${N}_{c}$ limit in holography reduces the DBM to a folded feed-forward architecture. We also neurally implement holographic renormalization into an autoencoder. The DBM for the $\mathrm{AdS}/\mathrm{CFT}$ may serve as a platform for studying mechanisms of spacetime emergence in holography.
Author: Koji Hashimoto
Institution: The University of Osaka
Language: Latvian
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W2922301641