Bulk reconstruction in AdS and Gel'fand-Graev-Radon Transform
Samrat Bhowmick, Koushik Ray, Siddhartha Sen
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.
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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