Carrollian HKLL reconstruction from boundary operators

Determine whether Carrollian bulk local states in the induced BMS$_3$ representation can be obtained by applying a reconstructed bulk operator to the vacuum, and establish whether local Carrollian conformal-field-theory operators suffice or nonlocal operators are required.

Background

The paper constructs massive spin-1 Carrollian bulk local states algebraically as descendant states in induced BMS3_3 representations and computes their pairings using algebraic duals. Unlike the AdS analysis, where the states are shown to agree with a global HKLL reconstruction, no corresponding operator-level reconstruction is established for Carrollian holography.

The unresolved issue is both whether a bulk operator acting on the vacuum reproduces the constructed induced states and what class of boundary operators can implement that reconstruction. The paper further indicates that, after identifying suitable boundary operators, one would need to construct a vector smearing kernel and compare matrix elements beyond vacuum states.

References

Can the Carrollian bulk local states be obtained by applying a reconstructed bulk operator to the vacuum, as in our AdS calculation? A first step is to identify CCFT operators whose action on a vacuum realizes the induced states constructed here, an issue also raised for scalar reconstruction in ref.\,. It remains unclear whether local boundary operators suffice or whether nonlocal operators are needed.

— Spin-1 Bulk Local States in AdS/CFT and Carrollian Holography  (2610.07548 - Hao et al., 6 Oct 2026) in Conclusion and discussion, paragraph beginning “HKLL reconstruction in flat spacetime”