# KEK Theory workshop 2018

17-20 December 2018
Kenkyu-Honkan bldg. 1F
Japan timezone
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# Contribution

Kenkyu-Honkan bldg. 1F - Kobayashi Hall

# Holography from field theories and a realization of AdS/CFT correspondence

## Speakers

• Prof. Sinya AOKI

## Description

I argue that the Anti-de-Sitter (AdS) geometry in $d+1$ dimensions naturally emerges from an arbitrary conformal field theory in $d$ dimensions using the free flow equation. I first show that an induced metric defined from the flowed field generally corresponds to the quantum information metric, called the Bures or Helstrom metric, if the flowed field is normalized appropriately. I next verify that the induced metric computed explicitly with the free flow equation always becomes the AdS metric when the theory is conformal. I also show that the conformal symmetry in $d$ dimensions converts to the AdS isometry in $d+1$ dimensions after $d$ dimensional quantum averaging. This guarantees the emergence of AdS geometry without explicit calculation. I finally discuss several extensions of this method including the latest results.