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

@inproceedings{Yang2022GUEVF, title={GUE via Frobenius Manifolds. I. From Matrix Gravity to Topological Gravity and Back}, author={Di Yang}, year={2022} }

. 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.

## References

SHOWING 1-10 OF 72 REFERENCES

### Frobenius manifolds and Virasoro constraints

- Mathematics
- 1998

Abstract. For an arbitrary Frobenius manifold, a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation. In…

### The Equivariant Gromov-Witten theory of P**1

- Mathematics
- 2002

We express all equivariant Gromov-Witten invariants of the projective line as matrix elements of explicit operators acting in the Fock space. As a consequence, we prove the equivariant theory is…

### Virasoro constraints for quantum cohomology

- Mathematics
- 1998

Eguchi-Hori-Xiong and S. Katz proposed a conjecture that the partition function of topological sigma model coupled to gravity is annihilated by infinitely many differential operators which form half…

### Gromov - Witten invariants and integrable hierarchies of topological type

- Mathematics
- 2013

We outline two approaches to the construction of integrable hierarchies associated with the theory of Gromov - Witten invariants of smooth projective varieties. We argue that a comparison of these…

### Hodge–GUE Correspondence and the Discrete KdV Equation

- MathematicsCommunications in Mathematical Physics
- 2020

We prove the conjectural relationship recently proposed in [9] between certain special cubic Hodge integrals of the Gopakumar--Mari\~no--Vafa type [17, 28] and GUE correlators, and the conjecture…

### Semisimple Frobenius structures at higher genus

- Mathematics
- 2000

In the context of equivariant Gromov-Witten theory of tori actions with isolated fixed points, we compute genus g > 1 Gromov-Witten potentials and their generalizations with gravitational…

### Gromov-Witten classes, quantum cohomology, and enumerative geometry

- Mathematics
- 1994

The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic…

### GROMOV - WITTEN INVARIANTS AND QUANTIZATION OF QUADRATIC HAMILTONIANS

- Mathematics
- 2001

We describea formalism based on quantizationof quadratichamil- tonians and symplectic actions of loop groups which provides a convenient home for most of known general results and conjectures about…

### Intersection theory on the moduli space of curves and the matrix airy function

- Mathematics
- 1992

We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical…

### The structure of 2D semi-simple field theories

- Mathematics
- 2012

I classify the cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of κ-classes and by an extension datum to the…