Hilbert space in the flat limit of AdS/CFT. II. Massless particles

@misc{nguyen2026hilbert,
  title = {{Hilbert space in the flat limit of AdS/CFT. II. Massless particles}},
  author = {Kevin Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40878},
  eprint = {2610.40878},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40878},
}

TY  - UNPB
TI  - Hilbert space in the flat limit of AdS/CFT. II. Massless particles
AU  - Kevin Nguyen
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40878
UR  - https://arxiv.org/abs/2610.40878
AB  - Building on Part I of this series, where we described the emergence of massive scattering states, we demonstrate how unitary lowest-weight representations 𝒟(Δ,s) of the conformal group with fixed dimension Δ and arbitrary integer spin s contract to massless Poincaré particle representations. This requires combining the Inönü--Wigner contraction so(2,3) → iso(1,3) with an infinite boost, in which case massless scattering states naturally emerge in a carrollian basis. For Δ>s+1, we find that 𝒟(Δ,s) contracts to the direct sum of massless particles of all spins s'≤ s. At the unitarity bound, lower-spin states become null so that 𝒟(s+1,s) contracts to a single massless particle representation carrying the two maximal helicities J=± s. In both cases, the inner product converges to the Poincaré-invariant one after a single helicity-independent rescaling, so that unitarity is preserved throughout the contraction.
ER  -