2020/08/31 by A. Andreev, A. Popolitov, A. Sleptsov +1 · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Connection (principal bundle) #Genus #Hermitian matrix #Hierarchy #Matrix (chemical analysis) #Matrix model #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Simple (philosophy) #hep-th #math-ph #math.AG #math.CO #math.MP
paper · pdf · open access · doi:10.1007/jhep12(2020)038
published in Journal of High Energy Physics 2020(12) (Springer Nature) · 26 pages, no figures
openalex created_date 2020/08/21 · arxiv created 2020/09/07 · openalex publication_date 2020/12/01 · arxiv updated 2022/03/15 · openalex updated_date 2026/08/05
We study ℏ expansion of the KP hierarchy following Takasaki-Takebe arXiv:hep-th/9405096 considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ℏ are τ-functions of the ℏ-KP hierarchy and the expansion in ℏ for the ℏ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ℏ-formulation of the KP hierarchy arXiv:1509.04472, arXiv:1512.07172 with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.