Flat holography and celestial shockwaves

TL;DR

This paper develops a holographic dictionary connecting bulk scalar fields in flat spacetime to dual operators on the celestial sphere, incorporating real-time dynamics and shockwave examples to advance flat holography understanding.

Contribution

It introduces a systematic flat/CFT holographic dictionary for Minkowski spacetime, relating bulk scalar modes to celestial operators with principal series dimensions, including real-time features.

Findings

Established a holographic dictionary for flat spacetime

Linked bulk scalar modes to celestial operators with principal series dimensions

Demonstrated the dictionary with a shock wave example

Abstract

In this paper we systematically develop the flat/CFT holographic dictionary, building on AdS/CFT holography. After analysing the behaviour of scalar field modes on hyperbolic slices of Minkowski and performing the holographic renormalisation for the associated onshell action, we obtain a holography dictionary between the bulk theory and the corresponding dual theory on the celestial sphere. We propose that a single scalar field in the bulk is dual to two series of operators on the celestial sphere; the scaling dimension of these operators takes values on the principal series. The real time features of the bulk theory, such as the dynamical and the casual structure, are encoded in the construction of correlation functions on the boundary via the coefficients of the bulk modes. Moreover, we will see that the two series of operators can be interpreted as ingoing and outgoing waves in the bulk. We illustrate our dictionary with the example of a single shock wave. Our results lay foundations for further computation within the flat/celestial CFT correspondence.