DOAJ Open Access 2020

Genus expansion of matrix models and ћ expansion of KP hierarchy

A. Andreev A. Popolitov A. Sleptsov A. Zhabin

Abstrak

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] 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 ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

Topik & Kata Kunci

Nuclear and particle physics. Atomic energy. Radioactivity

Penulis (4)

A. Andreev

A. Popolitov

A. Sleptsov

A. Zhabin

Format Sitasi

APA MLA BibTeX

Andreev, A., Popolitov, A., Sleptsov, A., Zhabin, A. (2020). Genus expansion of matrix models and ћ expansion of KP hierarchy. https://doi.org/10.1007/JHEP12(2020)038

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Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.1007/JHEP12(2020)038
Akses: Open Access ✓