The Gaudin model and the super Bethe ansatz for unitarizable modules over the general linear Lie (super)algebra

@misc{cao2026gaudin,
  title = {{The Gaudin model and the super Bethe ansatz for unitarizable modules over the general linear Lie (super)algebra}},
  author = {Bintao Cao and Wan Keng Cheong and Ngau Lam},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14176},
  eprint = {2609.14176},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14176},
}

TY  - UNPB
TI  - The Gaudin model and the super Bethe ansatz for unitarizable modules over the general linear Lie (super)algebra
AU  - Bintao Cao
AU  - Wan Keng Cheong
AU  - Ngau Lam
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.14176
UR  - https://arxiv.org/abs/2609.14176
AB  - Let 𝒜^bf z_g be the Gaudin algebra for the general linear Lie (super)algebra g with respect to a sequence bf z ∈ ℂ^ℓ of pairwise distinct complex numbers, and let 𝕃 be any ℓ-fold tensor product of (infinite-dimensional) unitarizable highest weight g-modules. Fix a singular weight ξ of 𝕃. We show that the singular weight space 𝕃^sing_ξ is a cyclic 𝒜^bf z_g-module, and that the Gaudin algebra (𝒜^bf z_g)_𝕃^sing_ξ for 𝕃^sing_ξ is a Frobenius algebra. We also show that (𝒜^bf z_g)_𝕃^sing_ξ is diagonalizable with a simple spectrum for a generic bf z. Furthermore, we establish a super version of the Bethe ansatz for 𝒜^bf z_g on 𝕃^sing_ξ.
ER  -