I'm trying to get a global idea of the world of conformal field theories.

Many authors restrict attention to *CFT*s where the algerbas of left and right movers agree. I'd like to increase my intuition for the cases where that fails (i.e. heterotic *CFT*s).

What are the simplest models of heterotic *CFT*s?

There exist beautiful classification results (due to Fuchs-Runkel-Schweigert) in the non-heterotic case that say that rational

*CFT*s with a prescribed chiral algebras are classified by Morita equivlence classes of Frobenius algebras (a.k.a.

*Q*-systems) in the corresponding modular category.

Is anything similar available in the heterotic case?

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