Matrix models for stationary Gromov-Witten invariants of the Riemann sphere

Abstract

Inspired by recent formulæ of Dubrovin, Yang, and Zagier, we interpret the tau function enumerating stationary Gromov-Witten invariants of ${\mathbb{P}}^1$ as an isomonodromic tau function associated with a difference equation. As a byproduct we obtain an analogue of the Kontsevich matrix model for this tau function. A connection with the Charlier ensemble is also considered.

arXiv commentv3: new appendix B

References in corpus (22)

• Topological Strings and Integrable Hierarchies
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• The intrinsic normal cone
• The Topological CP^1 Model and the Large-N Matrix Integral
• Combinatorics of the Modular Group II: the Kontsevich integrals
• Products and Ratios of Characteristic Polynomials of Random Hermitian Matrices
• Extended Seiberg-Witten Theory and Integrable Hierarchy
• Virasoro Symmetries of the Extended Toda Hierarchy
• Characteristic polynomials of real symmetric random matrices
• Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$
• The dependence on the monodromy data of the isomonodromic tau function
• Open intersection numbers, Kontsevich-Penner model and cut-and-join operators
• Characteristic polynomials of random matrices at edge singularities
• Open intersection numbers, matrix models and MKP hierarchy
• Refined open intersection numbers and the Kontsevich-Penner matrix model
• On an Airy matrix model with a logarithmic potential
• Brezin-Gross-Witten tau function and isomonodromic deformations
• Darboux transformations and random point processes
• The Kontsevich-Penner matrix integral, isomonodromic tau functions and open intersection numbers
• WKB solutions of difference equations and reconstruction by the topological recursion
• The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon
• Universality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles

Cited by in corpus (1)

• Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method