• Corpus ID: 248505842

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}
}
  • Di Yang
  • Published 3 May 2022
  • Mathematics
. 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

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

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

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

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

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

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

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

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

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

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
...