Derives finite-energy hard celestial current algebra and its one-cocycle from the BMS dipole Ward identity, mapping the hard-hard residue to a two-particle primary module via Plancherel transform.
Shadow celestial operator product expansions
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Constructs bulk scalar field representations in Lorentzian AdS4 from boundary primaries via time-ordered propagators and derives their flat-space limits to plane-wave or Carrollian bases.
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