Flat Holography & Holographic Renormalization: Scalar Field
Martin Ammon, Federico Capone, Christoph Sieling
TL;DR
The paper develops a flat-space holographic renormalization framework for a real scalar in Minkowski spacetime with scattering boundary conditions, using a Hamilton-Jacobi approach to define a finite on-shell action and a GKPW-like dictionary. It identifies the dual Carrollian operator’s expectation value with the renormalized radial momentum and ties its source to AFS scattering data via a radial foliation. For free fields, it constructs the holographic two-point function and extends to massive fields, then outlines a perturbative scheme for interactions, including a tree-level three-point function computed from bulk-boundary propagators. The work reveals key differences from AdS/CFT, notably the exponential divergences and nonlocal counterterms, and proposes a path toward reconstructing bulk S-matrices from flat-holographic data.
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.