Schur Q-Polynomials and Kontsevich-Witten Tau Function
Algebraic Geometry
2022-06-24 v4 Mathematical Physics
Differential Geometry
math.MP
Abstract
Using matrix model, Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau-function as a linear expansion of Schur Q-polynomials. In this paper, we will show directly that the Q-polynomial expansion in this formula satisfies the Virasoro constraints, and consequently obtain a proof of this formula without using matrix model. We also give a proof for Alexandrov's conjecture that Kontsevich-Witten tau-function is a hypergeometric tau-function of the BKP hierarchy after re-scaling.
Cite
@article{arxiv.2103.14318,
title = {Schur Q-Polynomials and Kontsevich-Witten Tau Function},
author = {Xiaobo Liu and Chenglang Yang},
journal= {arXiv preprint arXiv:2103.14318},
year = {2022}
}
Comments
45 pages. Improved presentation, and corrected typos