An Application of Mirror Extensions

Abstract

In this paper we apply our previous results of mirror extensions to obtain realizations of three modular invariants constructed by A. N. Schellekens by holomorphic conformal nets with central charge equal to 24.

On Examples of Intermediate Subfactors from Conformal Field Theory

“…These ω li with i even will generate local simple currents (cf Definition 2.3 and Prop. 2.15 of [36]), and it follows that the left local support of c is nontrivial if li = 0modn for some even i. So we conclude that 2l = 0modn, and…”

“….3 and Prop. 2.15 of[36]), and it follows that the left local support of c is nontrivial if li = 0modn for some even i. So we conclude that 2l = 0modn, and [cc] =[1] + [ω m ].Note that there are λ 1 , λ 2 such thatc 1 ≺ λ 1 c,c 2 ∈ λ 2 c. From c 1 , λ 1 c = c 1c , λ 1 ≥ 1, we have d c 1 √ 2 ≥ d λ 1 , and similarly dc 2 √ 2 ≥ d λ 2 .…”

Quantum Symmetries for Exceptional SU(4) Modular Invariants Associated with Conformal Embeddings

“…This is actually so in all examples studied here, and in particular for the SU(4) ⊂ Spin (20) case which can also be recognized as the smallest member (n = 1) of a D 2n+1 ⊂ D (n+1)(4n+1) family of conformal embeddings appearing on table 4 of the standard reference [3], and on table II(a) of the standard reference [38], since SU(4) ≃ Spin(6). This embedding, which is "special" (i.e., non regular: unequal ranks and Dynkin index not equal to 1), does not seem to be quoted in other standard references on conformal embeddings (for instance [24,27,40]), although it is explicitly mentioned in [1] and although its rank-level dual is indirectly used in case 18 of [37], or in [43]. The corresponding SU(4) modular invariant was later recovered by [31], using arithmetical methods, and used to determine the E 8 (SU(4)) quantum graph, but since the existence of an associated conformal embedding had slipped into oblivion, it was incorrectly stated that this particular example could not be obtained from conformal embedding considerations.…”

Examples of Subfactors from Conformal Field Theory

“…Many examples on this list have been realized (cf. [31,32,11], [55]). We note that the examples in [31,32,11] [10]).…”

“…Many examples on this list have been realized (cf. [31,32,11], [55]). We note that the examples in [31,32,11] are given in the language of lattice VOAs, their orbifolds, and affine Kac-Moody algebras.…”