Bulk Reconstruction of Scalar Excitations in Flat$_3$/CCFT$_2$ and the Flat Limit from (A)dS$_3$/CFT$_2$

TL;DR

The paper demonstrates that bulk local scalar excitations in $Flat_3$ can be reconstructed from $CCFT_2$ states, identifying the induced representation as the correct dual for massive scalars. It shows that this approach reproduces the bulk spectrum and bulk-to-bulk propagator, and it establishes a novel flat limit from both $AdS_3$/CFT_2 and $dS_3$/CFT_2 that maps highest-weight representations to the induced one and preserves the Green's functions. The results provide a self-consistent picture of flat holography, including an information-metric derivation of the bulk flat metric from CCFT_2 states and evidence that the dual theory remains unitary in this sector. The work also lays groundwork for HKLL-like reconstructions in flat holography and suggests a new, general mechanism for relating boundary Carrollian theories to bulk flat geometries across AdS/dS limits.

Abstract

We explore the reconstruction of bulk local states in three-dimensional flat spacetime (Flat$_3$) using states from two-dimensional Carrollian conformal field theories (CCFT$_2$), proposed as dual field theories in one lower dimension. For massive scalar-type bulk excitations, reconstruction is achieved through states in the induced representation. This method successfully reproduces the bulk massive scalar spectrum and the bulk-to-bulk propagator. Additionally, we identify a new flat limit from AdS$_3$ and dS$_3$ spacetimes, further validating our proposal for scalar reconstruction in Flat$_3$/CCFT$_2$.

Figures (1)

• Figure 1: Penrose diagram of Mikowski space coordinated by \ref{['eq: 3d flat metric in the retarded coordinate']}.