Dual geometry of entanglement entropy via deep learning

For a given entanglement entropy of quantum field theory, we investigate how to reconstruct its dual geometry by applying the Ryu-Takayanagi formula and the deep learning method. In the holographic setup, the radial coordinate is identified with the energy scale of the dual quantum field theory. Therefore, the holographic dual geometry can describe how physical properties of a quantum field theory change along the renormalization group flow. Intriguingly, we show that the reconstructed geometry only from the entanglement entropy data can give us more information about other physical properties like thermodynamic quantities in the infrared region.