Scale Holography

TL;DR

This paper introduces a novel scale holography framework linking d-dimensional dynamical systems to (d+1)-dimensional local systems, facilitating the study of non-local theories through higher-dimensional duals, exemplified by p-adic strings.

Contribution

It proposes a new scale-holographic correspondence with an explicit dimensionful constant, enabling local descriptions of non-local theories in higher dimensions.

Findings

Establishes a new scale holography relation.

Demonstrates the duality with p-adic string theory.

Provides a method to study non-local theories via local higher-dimensional systems.

Abstract

We present a new correspondence between a d-dimensional dynamical system and a whole family of (d+1)-dimensional systems. This new scale-holographic relation is built by the explicit introduction of a dimensionful constant which determines the size of the additional dimension. Scale holography is particularly useful for studying non-local theories, since the equivalent dual system on the higher dimensional manifold can be made to be local, as we illustrate with the specific example of the p-adic string.