A holographic reduction of Minkowski space-time

TL;DR

The paper proposes a holographic reduction of Minkowski space by slicing it into AdS and dS spaces, with all slices sharing the light-cone boundaries $S^-_d$ and $S^+_d$. It shows that bulk scalar fields decompose into a continuum of conformal operators on these two spheres, enabling a Minkowski/CFT-like correspondence that can reconstruct Green's functions and the S-matrix from boundary correlators, even in the presence of interactions. A detailed analysis of asymptotic symmetries reveals a conformal structure on the light-cone boundary and identifies BMS as a subalgebra of the bulk diffeomorphisms, while a gravity extension is explored through a 2+1 dimensional example and Brown–York-type boundary data. The work provides a concrete framework for holography in flat space, clarifying how information about the bulk can be encoded on null boundaries and offering a path toward incorporating gravity and more general spacetimes.

Abstract

Minkowski space can be sliced, outside the lightcone, in terms of Euclidean Anti-de Sitter and Lorentzian de Sitter slices. In this paper we investigate what happens when we apply holography to each slice separately. This yields a dual description living on two spheres, which can be interpreted as the boundary of the light cone. The infinite number of slices gives rise to a continuum family of operators on the two spheres for each separate bulk field. For a free field we explain how the Green's function and (trivial) S-matrix in Minkowski space can be reconstructed in terms of two-point functions of some putative conformal field theory on the two spheres. Based on this we propose a Minkowski/CFT correspondence which can also be applied to interacting fields. We comment on the interpretation of the conformal symmetry of the CFT, and on generalizations to curved space.

Figures (2)

• Figure 1: Inside light-cone (d+2)-dimensional Minkowski space-time can be sliced with Euclidean anti-de Sitter spaces $H_{d+1}$ while out-side the light-cone the appropriate slices are Loretzian de Sitter spaces $dS_{d+1}$. The only boundaries of the slices are either sphere $S^-_d$ or sphere $S^+_d$ lying at infinity of the light-cone.
• Figure 2: The asymptotic hypersurfaces $\Sigma_{\tt in}$ and $\Sigma_{\tt out}$ are defined in a small vicinity of the past and future infinity of the light-cone respectively.