Topological Field Theory approach to the Generalized Benney Hierarchy

TL;DR

This paper explores the integrability of the generalized Benney hierarchy using topological field theory methods, deriving free energy, correlation functions, and genus-one corrections to its Poisson brackets.

Contribution

It introduces a novel approach linking topological field theories with the generalized Benney hierarchy, including genus-one corrections and explicit formulations.

Findings

Primary free energy and correlation functions at genus zero are obtained.

Genus-one corrections to the Poisson brackets are explicitly derived.

The approach connects Landau-Ginzburg formulation with integrable hierarchy analysis.

Abstract

The integrability of the generalized Benney hierarchy with three primary fields is investigated from the point of view of two-dimensional topological field theories coupled to gravity. The associated primary free energy and correlation functions at genus zero are obtained via Landau-Ginzburg formulation and the string equation is derived using the twistor construction for the Orlov operators. By adopting the approach of Dubrovin and Zhang we obtain the genus-one corrections of the Poisson brackets of the generalized Benney hierarchy.