Galois modular invariants of WZW models

Fuchs, Juergen; Schellekens, A.N.; Schweigert, Christoph

doi:10.1016/0550-3213(94)00577-2

Cited by 36 publications

(66 citation statements)

References 44 publications

(79 reference statements)

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“…However, it does not seem reasonable to expect that there are associated nets of subfactors for all type I modular invariants. In fact there are type I modular invariants for which there is no "fixed point resolution" of the S-matrix, see [16,Sect. 4].…”

Section: Non-degenerate Braidings On Orbifold Graphsmentioning

confidence: 99%

Modular Invariants, Graphs and α-Induction¶for Nets of Subfactors. III

Böckenhauer¹,

Evans²

1999

Commun. Math. Phys.

113

321

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In this paper we further develop the theory of α-induction for nets of subfactors, in particular in view of the system of sectors obtained by mixing the two kinds of induction arising from the two choices of braiding. We construct a relative braiding between the irreducible subsectors of the two "chiral" induced systems, providing a proper braiding on their intersection. We also express the principal and dual principal graphs of the local subfactors in terms of the induced sector systems. This extended theory is again applied to conformal or orbifold embeddings of SU (n) WZW models. A simple formula for the corresponding modular invariant matrix is established in terms of the two inductions, and we show that it holds if and only if the sets of irreducible subsectors of the two chiral induced systems intersect minimally on the set of marked vertices, i.e. on the "physical spectrum" of the embedding theory, or if and only if the canonical endomorphism sector of the conformal or orbifold inclusion subfactor is in the full induced system. We can prove either condition for all simple current extensions of SU (n) and many conformal inclusions, covering in particular all type I modular invariants of SU (2) and SU (3), and we conjecture that it holds also for any other conformal inclusion of SU (n) as well. As a by-product of our calculations, the dual principal graph for the conformal inclusion SU (3) 5 ⊂ SU (6) 1 is computed for the first time.

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Section: Non-degenerate Braidings On Orbifold Graphsmentioning

confidence: 99%

Modular Invariants, Graphs and α-Induction¶for Nets of Subfactors. III

Böckenhauer¹,

Evans²

1999

Commun. Math. Phys.

113

321

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“…It is not known if modular invariants that are simple current invariants in the sense of [38,45], but not simple current invariants in our sense, can appear as torus partition functions of consistent conformal field theories. (A class of examples of modular invariants of this type that are definitely unphysical has been found in section 4 of [46]. )…”

Section: Restriction To Invertible Subobjectsmentioning

confidence: 99%

TFT construction of RCFT correlatorsIII: simple currents

2004

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We use simple currents to construct symmetric special Frobenius algebras in modular tensor categories. We classify such simple current type algebras with the help of abelian group cohomology. We show that they lead to the modular invariant torus partition functions that have been studied by Kreuzer and Schellekens. We also classify boundary conditions in the associated conformal field theories and show that the boundary states are given by the formula proposed in hep-th/0007174. Finally, we investigate conformal defects in these theories.

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“…In [11] we considered orbifolds at radius R 2 = 2pq (p, q odd primes) (with pq +7 primaries), and considered the automorphism that occurs [31], [21] if the radius factorizes into two primes.…”

Section: Examples Iii: C=1 Orbifoldsmentioning

confidence: 99%

Orientation matters for NIMreps

Sousa¹,

Schellekens²

2003

Nuclear Physics B

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The problem of finding boundary states in CFT, often rephrased in terms of "NIMreps" of the fusion algebra, has a natural extension to CFT on non-orientable surfaces.This provides extra information that turns out to be quite useful to give the proper interpretation to a NIMrep. We illustrate this with several examples. This includes a rather detailed discussion of the interesting case of the simple current extension of A 2 level 9, which is already known to have a rich structure. This structure can be disentangled completely using orientation information. In particular we find here and in other cases examples of diagonal modular invariants that do not admit a NIMrep, suggesting that there does not exist a corresponding CFT. We obtain the complete set of NIMreps (plus Moebius and Klein bottle coefficients) for many exceptional modular invariants of WZW models, and find an explanation for the occurrence of more than one NIMrep in certain cases. We also (re)consider the underlying formalism, emphasizing the distinction between oriented and unoriented string annulus amplitudes, and the origin of orientation-dependent degeneracy matrices in the latter.

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Galois modular invariants of WZW models

Cited by 36 publications

References 44 publications

Modular Invariants, Graphs and α-Induction¶for Nets of Subfactors. III

Modular Invariants, Graphs and α-Induction¶for Nets of Subfactors. III

TFT construction of RCFT correlatorsIII: simple currents

Orientation matters for NIMreps

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