Topological conformal field theory with a rational W potential and the dispersionless KP hierarchy

TL;DR

This paper introduces a new class of topological conformal field theories characterized by a rational W potential, derived from the dispersionless KP hierarchy, unifying minimal models and revealing universal structures.

Contribution

It formulates a novel class of TCFTs with rational W potentials and explicitly solves the dispersionless KP hierarchy to find these potentials, including their universal form in large phase spaces.

Findings

Derived explicit W potentials from the dispersionless KP hierarchy.

Unified minimal models of A and D types within a new TCFT class.

Showed W potential's universal form independent of specific solutions.

Abstract

We present a new class of topological conformal field theories (TCFT) characterized by a rational $W$ potential, which includes the minimal models of A and D types as its subclasses. An explicit form of the $W$ potential is found by solving the underlying dispersionless KP hierarchy in a particular small phase space. We discuss also the dispersionless KP hierarchy in large phase spaces by reformulating the hierarchy, and show that the $W$ potential takes a universal form, which does not depend on a specific form of the solution in a large space.