Flat Holography & Holographic Renormalization: Scalar Field
arXiv:2512.14818 · doi:10.1007/JHEP07(2026)124
The paper develops a holographic renormalization framework for scalar fields in flat Minkowski space using the Hamilton‑Jacobi method, establishing a flat‑space holographic dictionary that relates boundary scattering data to bulk field dynamics.
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.
54 pages. Version published in JHEP