# "Old" Conformal Bootstrap on AdS: $O(N)$ symmetric scalar model

## TL;DR

This paper develops simplified conformal bootstrap equations within the AdS/CFT framework to compute conformal dimensions in the $O(N)$ symmetric scalar model, offering a novel approach that bypasses traditional Feynman-Witten diagrams.

## Contribution

It introduces a simplified set of bootstrap equations in AdS/CFT that facilitate calculations of conformal dimensions in the $O(N)$ model, using a Schwinger-Keldysh inspired formalism.

## Key findings

- Calculated conformal dimensions in the $O(N)$ model.
- Proposed a bootstrap approach compatible with Schwinger-Keldysh formalism.
- Provided a new method to analyze conformal correlators in AdS/CFT.

## Abstract

Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger-Keldysh formalism is used in AdS/CFT instead of conventional Feynman-Witten diagrams technique, permits to calculate values of conformal dimensions in the $O(N)$ symmetric model with conformal or composite Hubbard-Stratonovich field.