Intersection Theory , Integrable Hierarchies and Topological Field Theory ∗
نویسنده
چکیده
In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological field theory. We focus in particular on the question why matrix integrals of the type considered by Kontsevich naturally appear as τ -functions of integrable hierarchies related to topological minimal models. Lectures presented at the Cargèse Summer School on New Symmetry Principles in Quantum Field Theory, July 16-27, 1991. Research supported by the W.M. Keck Foundation
منابع مشابه
Finite Euler Hierarchies and Integrable Universal Equations
Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field theories, classical topological field theories – whose classical solutions span topological classes of manifolds – and reparametri-sation invariant theories – gener...
متن کاملBihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation
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 classical W -algebra; we compute the central charge of this algebra. We also express the generating function of elliptic Gromov Witten invariants via tau-function of the isomonodromy deformation problem arisin...
متن کاملIntegrable Systems and Classification of 2 - Dimensional Topological Field Theories
In this paper we consider from the point of view of differential geometry and of the theory of integrable systems the so-called WDVV equations as defining relations of 2-dimensional topological field theory. A complete classification of massive topological con-formal field theories (TCFT) is obtained in terms of monodromy data of an auxillary linear operator with rational coefficients. Procedur...
متن کاملActions for Integrable Systems and Deformed Conformal Theories*
I report on work on a Lagrangian formulation for the simplest 1+1 dimensional integrable hierarchies. This formulation makes the relationship between conformal field theories and (quantized) 1+1 dimensional integrable hierarchies very clear.
متن کاملEuler Hierarchies and Universal Equations
Finite Euler hierarchies of field theory Lagrangians leading to universal equations of motion for new types of string and membrane theories and for classical topological field theories are constructed. The analysis uses two main ingredients. On the one hand, there exists a generic finite Euler hierarchy for one field leading to a universal equation which generalises the Plebanski equation of se...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1992