Multiparticle States for the Flat Hologram

TL;DR

This paper explores the structure of multiparticle operators in Celestial CFT, extending the flat-space holographic dictionary and clarifying the nature of representations and operator expansions in the celestial holography framework.

Contribution

It constructs composite primaries in Celestial CFT from Carrollian and celestial perspectives, revealing new insights into multiparticle states and operator expansions.

Findings

Identification of multiparticle operators in celestial OPE

Clarification of primary conditions from Carrollian limits

Analysis of representation compatibility and unitarity

Abstract

We use the extrapolate dictionary to revisit the spectrum of operators in Celestial CFT. Under the Celestial CFT map, each state in the 4D Hilbert space should map to one in the 2D Hilbert space. This implies that, beyond the familiar single particle states/operators, there should be multiparticle operators appearing in the celestial OPE. We extend the existing flat-space dictionary by constructing composite primaries from both Carrollian and Celestial perspectives. In the process, we demonstrate some subtleties in deriving the Poincar\'e primary condition from the Carrollian limit, clarify the compatibility of principal series representations with highest weight representations and unitarity in Celestial CFT, and discuss how the celestial OPE block expansion emerges from a 2D CFT standpoint.