Renormalization Group and Curved Spacetime

Understand

We examine the role of curved geometry on renormalization group by means of image compression based on the singular value decomposition.

• By calculating course-grained images and their entanglement entropy, we find the anti-de Sitter space / conformal field theory correspondence hidden in the compression.
• The correspondence is originated from the conservation law for information.
• We discuss how one particular metric is automatically induced from various images.