01141nas a2200109 4500008004100000245005100041210005100092260001000143520082200153100002000975856003600995 1992 en d00aIntegrable systems in topological field theory0 aIntegrable systems in topological field theory bSISSA3 aIntegrability of the system of PDE for dependence on coupling parameters of the (tree-level) primary partition function in massive topological field theories, being imposed by the associativity of the perturbed primary chiral algebra, is proved. In the conformal case it is shown that all the topological field theories are classified as solutions of a universal high-order PainlevĂ©-type equation. Another integrable hierarchy (of systems of hydrodynamic type) is shown to describe coupling to gravity of the matter sector of any topological field theory. Different multicritical models with the given structure of primary correlators are identified with particular self-similar solutions of the hierarchy. The partition function of any of the models is calculated as the corresponding tau-function of the hierarchy.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/6477