Holography on local fields via Radon Transform

TL;DR

This paper extends holographic principles to local fields by defining Radon transforms on anti-de Sitter space over local fields, enabling bulk reconstruction of quantum fields through inverse Radon transforms, generalizing real-number cases.

Contribution

It introduces a novel Radon transform framework on anti-de Sitter space over local fields, facilitating holographic bulk reconstruction in this new setting.

Findings

Defined Radon transform on local fields over AdS space

Established inverse Radon transform for bulk reconstruction

Generalized holographic correspondence beyond real numbers

Abstract

We define Radon transform and its inverse on the two-dimensional anti-de Sitter space over local fields using a novel construction through a quadratic equation over the local field. We show that the holographic bulk reconstruction of quantum fields in this space can be formulated as the inverse Radon transform, generalizing the case over the reals, studied earlier.