Fortuitous BMN Cohomology at Every N

@misc{koch2026fortuitous,
  title = {{Fortuitous BMN Cohomology at Every $N$}},
  author = {Robert de Mello Koch and Minkyoo Kim and Sinong Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21592},
  eprint = {2610.21592},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21592},
}

TY  - UNPB
TI  - Fortuitous BMN Cohomology at Every N
AU  - Robert de Mello Koch
AU  - Minkyoo Kim
AU  - Sinong Liu
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.21592
UR  - https://arxiv.org/abs/2610.21592
AB  - Finite-N trace relations can produce Q-cohomology classes with no stable large-N ancestor. The brane-fused construction at SU(3) suggests that such states can retain an SU(2) nonabelian core accompanied by scalar hair. We develop this idea into a general construction for every SU(N), N≥3. Starting from the SU(2) threshold operator O_24, we select pairs of eigenvalues of one scalar and construct corrected two-colour letters whose Q-transformations obey the SU(2) rules exactly. Substitution into O_24 gives a closed rational operator for each pair. Multiplying by eigenvalue-separation factors removes the denominators, and summing over all pairs produces a gauge-invariant polynomial. An exact block-restriction identity recovers a nonzero multiple of O_24. The restriction maps every stable class to a stable SU(2) class, proving that the resulting operator is non-exact and fortuitous, even when non-Coulombic stable classes are included. This proves the existence of fortuitous BMN cohomology at every N≥3. The construction is an exact algebraic realization of a nonabelian core with scalar dressing.
ER  -