Rationally weighted Hurwitz numbers, Meijer $G$-functions and matrix integrals

Abstract

The quantum spectral curve equation associated to KP $\tau$-functions of hypergeometric type serving as generating functions for rationally weighted Hurwitz numbers is solved by generalized hypergeometric series. The basis elements spanning the corresponding Sato Grassmannian element are shown to be Meijer $G$-functions, or their asymptotic series. Using their Mellin integral representation the $\tau$-function, evaluated at the trace invariants of an externally coupled matrix, is expressed as a matrix integral.

24 pages. References brought up to date

References in corpus (5)

• On KP-integrable Hurwitz functions
• Virasoro constraints for Kontsevich-Hurwitz partition function
• The matrix model for hypergeometric Hurwitz numbers
• Fermionic approach to weighted Hurwitz numbers and topological recursion
• Spectral curves for hypergeometric Hurwitz numbers

Cited by in corpus (5)

• Weighted Hurwitz numbers and topological recursion
• Constellations and $\tau$-functions for rationally weighted Hurwitz numbers
• Generating weighted Hurwitz numbers
• Matrix model generating function for quantum weighted Hurwitz numbers
• Weighted Hurwitz numbers, $\tau$-functions and matrix integrals