# Bulk reconstruction in AdS and Gel'fand-Graev-Radon Transform

## TL;DR

This paper explores how bulk reconstruction in Euclidean AdS space can be achieved through the inverse Gel'fand-Graev-Radon transform, linking boundary correlation functions to bulk field theories at various loop levels.

## Contribution

It establishes a direct connection between bulk reconstruction in AdS and the Gel'fand-Graev-Radon transform, providing a new mathematical framework for relating boundary and bulk correlators.

## Key findings

- Bulk reconstruction formula derived from the inverse Radon transform.
- Boundary correlators related to bulk scalar field correlators at multiple loop orders.
- Mathematical framework for connecting boundary CFT and bulk AdS fields.

## Abstract

The bulk reconstruction formula for a Euclidean anti-de Sitter space is directly related to the inverse of the Gel'fand-Graev-Radon transform. Correlation functions of a conformal scalar field theory in the boundary are thereby related to correlation functions of a self-interacting scalar field theory in the bulk at different loop orders.

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Source: https://tomesphere.com/paper/1705.06985