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arXiv · 2204.06855

Special flow equation and GKP-Witten relation

Sinya Aoki·Janos Balog·Tetsuya Onogi·Shuichi Yokoyama
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Abstract

We develop a framework for the reconstruction of the bulk theory dual to conformal field theory (CFT) without any assumption by means of a flow equation. To this end we investigate a minimal extension of the free flow equation and find that at a special parametrization the conformal transformation for a normalized smeared operator exactly becomes the isometry of anti-de Sitter space (AdS). By employing this special flow equation to O$(N)$ vector models, we explicitly show that the AdS geometry as well as the scalar field satisfying the GKP-Witten relation concurrently emerge in this framework.

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Sinya Aoki, Janos Balog, Tetsuya Onogi, Shuichi Yokoyama. 2022-04-14. Special flow equation and GKP-Witten relation. https://arxiv.org/abs/2204.06855

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