The Annihilating Ideals of Minimal Models

Abstract

We describe several aspects of the annihilating ideals and reduced chiral algebras of conformal field theories, especially, minimal models of Wn algebras. The structure of the annihilating ideal and a vanishing condition is given. Using the annihilating ideal, the structure of quasi-finite models of the Virasoro (2,q) minimal models are studied, and their intimate relation to the Gordon identities are discussed. We also show the examples in which the reduced algebras of Wn and Wℓ algebras at the same central charge are isomorphic to each other.

Superconformal index, BPS monodromy and chiral algebras

“…The r.h.s. of (7.25) is the Feigin-Nakanishi-Ooguri formula for the vacuum character of the (2, 2n + 3) Virasoro minimal model [56,57]. This confirms the claim of [9] that Tr M(q) −1 is equal to the vacuum character of the minimal model.…”

Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory

“…Fermionic representations have been derived for classes of rational conformal theories defined as cosets of affine Lie algebras [19] and in particular for the series of non-unitary minimal models M (2, 2p + 3) [21]. These representations follow by a quasi-particle interpretation based on the Bethe Ansatz description and give alternative representations of the characters with respect to the Feigin-Fuchs-Felder construction [22].…”

An Algebraic Approach to Logarithmic Conformal Field Theory

“…We can expand this condition in terms of modes; the first non-trivial condition is then simply that the zero mode of the null-vector N annihilates every allowed state in the representation (see also [52]). It is most convenient to evaluate this condition on a highest weight state; in this case the zero mode of N can be easily calculated, and one finds that…”