On Dubrovin Topological Field Theories

TL;DR

This paper explores the relationship between Dubrovin's topological field theories linked to Coxeter groups and standard ADE solutions, revealing a restriction-based construction and connections to conformal field theory operator algebras.

Contribution

It demonstrates that Dubrovin's theories can be derived from ADE solutions via restriction and investigates their algebraic structures and connections to conformal field theories.

Findings

Dubrovin theories are obtainable by restricting ADE solutions.

Coxeter graphs and matrices appear in dual algebras.

Connections with conformal field theory operator algebras are discussed.

Abstract

I show that the new topological field theories recently associated by Dubrovin with each Coxeter group may be all obtained in a simple way by a ``restriction'' of the standard ADE solutions. I then study the Chebichev specializations of these topological algebras, examine how the Coxeter graphs and matrices reappear in the dual algebra and mention the intriguing connection with the operator product algebra of conformal field theories. A direct understanding of the occurrence of Coxeter groups in that context is highly desirable.