English

BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions

Exactly Solvable and Integrable Systems 2022-07-06 v4 Mathematical Physics math.MP

Abstract

We derive a formula for the connected nn-point functions of a tau-function of the BKP hierarchy in terms of its affine coordinates. This is a BKP-analogue of a formula for KP tau-functions proved by Zhou in [arXiv:1507.01679]. Moreover, we prove a simple relation between the KP-affine coordinates of a tau-function τ(t)\tau(\mathbf{t}) of the KdV hierarchy and the BKP-affine coordinates of τ(t/2)\tau(\mathbf{t}/2). As applications, we present a new algorithm to compute the free energies of the Witten-Kontsevich tau-function and the Br\'ezin-Gross-Witten tau-function.

Keywords

Cite

@article{arxiv.2201.08178,
  title  = {BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions},
  author = {Zhiyuan Wang and Chenglang Yang},
  journal= {arXiv preprint arXiv:2201.08178},
  year   = {2022}
}
R2 v1 2026-06-24T08:56:33.825Z