GUE via Frobenius Manifolds. I. From Matrix Gravity to Topological Gravity and Back

TL;DR

This paper provides a direct proof linking GUE partition functions with Gromov-Witten invariants of the complex projective line, advancing understanding of topological and matrix gravity through a comprehensive diagram.

Contribution

It offers a direct proof of Dubrovin's relationship and summarizes recent progress in topological and matrix gravity in a visual diagram.

Findings

Confirmed the connection between GUE and Gromov-Witten invariants

Presented a comprehensive diagram of recent progress in topological and matrix gravity

Enhanced understanding of the interplay between matrix models and topological field theories

Abstract

Dubrovin establishes the relationship between the GUE partition function and the partition function of Gromov--Witten invariants of the complex projective line. In this paper, we give a direct proof of Dubrovin's result. We also present in a diagram the recent progress on topological gravity and matrix gravity.