## 316 Citations

On structure and open problems in topological theories coupled to topological gravity

- Mathematics
- 1994

The structure of topological theory coupled to topological gravity is studied. We show that in this theoryQ-exact terms do not decouple. This nondecoupling in the action of the theory is connected…

Geometry and integrability of topological-antitopological fusion

- Mathematics
- 1993

Integrability of equations of topological-antitopological fusion (being proposed by Cecotti and Vafa) describing the ground state metric on a given 2D topological field theory (TFT) model, is proved.…

On classification ofN=2 supersymmetric theories

- Mathematics, Physics
- 1993

We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling…

Flat coordinates of topological conformal field theory and solutions of the Gauss–Manin system

- Mathematics
- 2016

It was shown many years ago by Dijkgraaf, Velinde, and Verlinde for two-dimensional topological conformal field theory and more recently for the non-critical String theory that some models of these…

Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation

- Mathematics
- 1998

Abstract:We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a…

On the Geometry of Singularities in Quantum Field Theory

- Mathematics
- 2011

This survey investigates the geometry of singularities from the viewpoint of conformal and topological quantum field theory and string theory. First, some classical results concerning simple surface…

On integrable systems and supersymmetric gauge theories

- Physics, Mathematics
- 1996

We discuss the properties ofN=2 supersymmetric gauge theories underlying the Seiberg-Witten hypothesis. We consider the main points of the theory that describes the finite-gap solutions to integrable…

Compatible poisson structures of hydrodynamic type and the equations of associativity in two-dimensional topological field theory

- Mathematics
- 1999

The Nonlinear Graviton as an Integrable System

- Mathematics
- 1998

The curved twistor theory is studied from the point of view of integrable systems.
A twistor construction of the hierarchy associated with the anti-self-dual Einstein vacuum equations (ASDVE) is…

## References

SHOWING 1-10 OF 28 REFERENCES

Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginsburg models

- Physics
- 1992

We show that the bi-hamiltonian structure of the averaged Gelfand-Dikii hierarchy is involved in the Landau-Ginsburg topological models (forAn-Series): the Casimirs for the first P.B. give the…

Topological quantum field theory

- Physics, Mathematics
- 1988

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in…

Notes on topological string theory and 2-D quantum gravity

- Physics
- 1990

In these notes we give a review of topological string theory. We discuss twodimensional topological field theories, which represent its classical backgrounds. We describe their symmetries and the…

Hamiltonian methods in the theory of solitons

- Mathematics
- 1987

The Nonlinear Schrodinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples…

CONTINUUM SCHWINGER-DYSON EQUATIONS AND UNIVERSAL STRUCTURES IN TWO-DIMENSIONAL QUANTUM GRAVITY

- Physics, Mathematics
- 1991

We study the continuum Schwinger-Dyson equations for nonperturbative two-dimensional quantum gravity coupled to various matter fields. The continuum Schwinger-Dyson equations for the one-matrix model…

Monodromy- and spectrum-preserving deformations I

- Mathematics
- 1980

A method for solving certain nonlinear ordinary and partial differential equations is developed. The central idea is to study monodromy preserving deformations of linear ordinary differential…

Nonperturbative two-dimensional quantum gravity.

- Physics, MathematicsPhysical review letters
- 1990

We propose a nonperturbative definition of two-dimensional quantum gravity, based on a double-scaling limit of the random-matrix model. We derive an exact differential equation for the partition…

Spectral theory of two-dimensional periodic operators and its applications

- Mathematics
- 1989

CONTENTS Introduction Chapter I. The spectral theory of the non-stationary Schrodinger operator § 1. The perturbation theory for formal Bloch solutions § 2. The structure of the Riemann surface of…

Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation

- Mathematics
- 1980

Inverse spectral theory is used to prescribe and study equations for the slow modulations of N-phase wave trains for the Korteweg-de Vries (KdV) equation. An invariant representation of the…