Code conformal field theory and framed algebra

TL;DR

This paper introduces code conformal field theories and framed algebras, establishing an equivalence between their categories and constructing new integrable models for studying moduli spaces.

Contribution

It defines framed algebras and proves their categorical equivalence with code conformal field theories, leading to new integrable models.

Findings

Categorical equivalence between framed algebras and code conformal field theories

Construction of new integrable conformal field theories

Potential applications to moduli space studies

Abstract

It is known that there are 48 Virasoro algebras acting on the monster conformal field theory. We call conformal field theories with such a property, which are not necessarily chiral, code conformal field theories. In this paper, we introduce a notion of a framed algebra, which is a finite-dimensional non-associative algebra, and showed that the category of framed algebras and the category of code conformal field theories are equivalent. We have also constructed a new family of integrable conformal field theories using this equivalence. These conformal field theories are expected to be useful for the study of moduli spaces of conformal field theories.