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Concavity of Normalized Generalized Brézin--Gross--Witten Correlators and Its Applications

  • Chenglang Yang
  • Xuhui Zhang
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Abstract

In this paper, we study the generalized Brézin--Gross--Witten model using its BKP integrability. By virtue of the formula for connected n-point functions of tau-functions of the BKP hierarchy obtained by Wang and the first-named author, we prove that the normalized generalized BGW correlators are strictly concave for fixed genus and fixed total degree. As applications, we establish the strict Schur-concavity and derive upper and lower bounds for these correlators. We also prove the strict monotonicity of normalized ordinary BGW correlators, which resolves a conjecture by Guo--Norbury--Yang--Zagier.

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Cite

BibTeXRIS
BibTeX
@misc{yang2026concavity,
  title = {{Concavity of Normalized Generalized Brézin--Gross--Witten Correlators and Its Applications}},
  author = {Chenglang Yang and Xuhui Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06675},
  eprint = {2611.06675},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06675},
}
RIS
TY  - UNPB
TI  - Concavity of Normalized Generalized Brézin--Gross--Witten Correlators and Its Applications
AU  - Chenglang Yang
AU  - Xuhui Zhang
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06675
UR  - https://arxiv.org/abs/2611.06675
AB  - In this paper, we study the generalized Brézin--Gross--Witten model using its BKP integrability. By virtue of the formula for connected n-point functions of tau-functions of the BKP hierarchy obtained by Wang and the first-named author, we prove that the normalized generalized BGW correlators are strictly concave for fixed genus and fixed total degree. As applications, we establish the strict Schur-concavity and derive upper and lower bounds for these correlators. We also prove the strict monotonicity of normalized ordinary BGW correlators, which resolves a conjecture by Guo--Norbury--Yang--Zagier.
ER  -