Flat Space Physics from AdS Actions

TL;DR

This paper explores flat space holography by reducing 4D scalar actions to 3D slices with hyperbolic geometry, revealing continuous spectra and boundary behaviors linked to lightcone and null infinity limits.

Contribution

It introduces a method to derive flat space holographic dualities through slice-by-slice reduction of 4D actions, connecting boundary terms and asymptotic behaviors.

Findings

Reduced 4D actions exhibit continuous spectra from noncompact reduction.

Boundary terms relate different asymptotic limits of fields.

Massive and massless cases show distinct boundary mode interpretations.

Abstract

Flat spacetimes are foliated by hyperbolic slices that are geometrically three-dimensional de Sitter or anti-de Sitter spaces. As such, it is possible to construct flat space holographic dualities by applying the AdS/CFT bulk-to-boundary dictionary slice by slice. In this work, we reduce 4D actions for massless scalars in both Minkowski space and Klein space and massive scalars in Minkowski space to actions on these 3D dS and AdS slices. In both Minkowski and Klein space, the reduced theories have a continuous spectrum of fields originating from the reduction over the noncompact $x^2$ direction. These actions are linked by boundary terms arising from field configurations discontinuous across the lightcone. In the massless case, different asymptotic limits of the reduced field near the boundary of the unit hyperbolic slice replicate either light cone or null infinity limits of the field; in the massive case, only one boundary mode of the reduced field has a simple geometric interpretation.