A simple construction of integrable Whitham type hierarchies

TL;DR

This paper introduces a straightforward method to construct Whitham type hierarchies across all genera, expressing their potentials as hypergeometric integrals and discussing potential generalizations to the universal moduli space.

Contribution

It presents a novel, simple construction of integrable Whitham hierarchies applicable to all genera, with potentials expressed via hypergeometric integrals.

Findings

Hierarchies constructed for all genera

Potentials expressed as hypergeometric integrals

Discussion on generalization to universal moduli space

Abstract

A simple construction of Whitham type hierarchies in all genera is suggested. Potentials of these hierarchies are written as integrals of hypergeometric type. Possible generalization for universal moduli space is also briefly discussed.