Algebras in tensor categories and coset conformal field theories

TL;DR

This paper discusses how recent algebraic methods in tensor categories enable a universal approach to constructing chiral data in coset conformal field theories, including complex maverick cases with exceptional modular invariants.

Contribution

It introduces a universal algebraic framework in tensor categories for coset CFTs, extending analysis to maverick cosets with exceptional modular invariants.

Findings

Universal construction of chiral data for coset theories

Application to maverick cosets with exceptional invariants

Advancement in algebraic understanding of conformal field theories

Abstract

The coset construction is the most important tool to construct rational conformal field theories with known chiral data. For some cosets at small level, so-called maverick cosets, the familiar analysis using selection and identification rules breaks down. Intriguingly, this phenomenon is linked to the existence of exceptional modular invariants. Recent progress in CFT, based on studying algebras in tensor categories, allows for a universal construction of the chiral data of coset theories which in particular also applies to maverick cosets.