Massless reconstruction in the Carrollian highest-weight representation

Determine whether a massless bulk local-state reconstruction exists in the Carrollian BMS$_3$ highest-weight representation, since the Casimir analysis does not establish either its existence or its absence.

Background

For massive spin-1 excitations, the paper proves that the BMS3_3 highest-weight representation admits only the zero state when the local covariance and massive Poincaré Casimir conditions are imposed. The massless limit is different: the Casimir constraints become degenerate and no longer force the contradiction used in the massive argument.

Consequently, the paper does not determine whether a nontrivial massless reconstruction can be realized in the highest-weight representation.

References

The Casimir comparison alone therefore establishes neither the existence nor the absence of a massless reconstruction.

— Spin-1 Bulk Local States in AdS/CFT and Carrollian Holography  (2610.07548 - Hao et al., 6 Oct 2026) in Section 4, subsection “Obstruction in the highest weight representation”