Generalized Fusion Potentials

TL;DR

This paper provides a criterion for when rational conformal field theories (RCFTs) can be described by generalized fusion potentials, showing that all RCFTs can be represented with multi-variable potentials as conjectured by Gepner.

Contribution

It introduces a simple criterion for the applicability of generalized fusion potentials and proves that all RCFTs can be described by multi-variable potentials.

Findings

A criterion for generalized fusion potential description is established.

All RCFTs can be represented by multi-variable fusion potentials.

Supports Gepner's conjecture on multi-variable potential descriptions.

Abstract

Recently, DiFrancesco and Zuber have characterized the RCFTs which have a description in terms of a fusion potential in one variable, and proposed a generalized potential to describe other theories. In this note we give a simple criterion to determine when such a generalized description is possible. We also determine which RCFTs can be described by a fusion potential in more than one variable, finding that in fact all RCFTs can be described in such a way, as conjectured by Gepner.