Flat Holography & Holographic Renormalization: Scalar Field

TL;DR

This paper develops a holographic renormalization method for scalar fields in Minkowski spacetime, establishing a flat-space holographic dictionary relating boundary data to bulk scattering information.

Contribution

It adapts the Hamilton-Jacobi holographic renormalization technique to flat spacetime scalar theories, creating a new framework for flat holography.

Findings

Derived a flat-space holographic dictionary linking boundary operators to bulk scattering data.

Extended the formalism to include massive and interacting scalar fields.

Commented on potential extensions to other bulk theories and backgrounds.

Abstract

We adapt the Hamilton-Jacobi method of holographic renormalization to scalar field theories in Minkowski spacetime with scattering boundary conditions. The approach yields a flat-space holographic dictionary in which the expectation value of a dual operator is given by the renormalized canonical momentum. The source of the operator is imposed as a Dirichlet condition in a radial timelike foliation of the bulk theory and corresponds to the scattering data appearing in the Arefeva-Faddeev-Slavnov generating functional. We initiate a study of massive scalars and interacting fields within this formalism and we comment on extensions to different bulk theories and backgrounds.