Level 1 WZW superselection sectors

Fuchs, Jürgen; Ganchev, Alexander; Vecsernyés, Péter

doi:10.1007/bf02097016

Cited by 14 publications

(36 citation statements)

References 16 publications

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“…For j = ℓ one has to read this result with (7.10), which means that our result only describes the sum of the irreducible characters χ (2) s and χ (2) c . By comparison with (9.10), we may also rewrite the result in the form (2) [j] (q) (9.17) for j = 1, 2, ... , ℓ.…”

Section: (96)mentioning

confidence: 99%

“…ofĤ NS into A-sectors, we can express the splitting ofĤ NS into tensor products of the Virasoro modules (10.3) and the irreducible highest weight modules of so(N) 2 (that is, H (2) • , H (2) v , H (2) [j] , and also H (2) s and H (2) c when N = 2ℓ) as follows. Our results show that for n = 0, 1, ... and j = 1, 2, ... , ℓ − 1.…”

Section: Decomposition Of the Tensor Productmentioning

confidence: 99%

“…Our results show that for n = 0, 1, ... and j = 1, 2, ... , ℓ − 1. When N = 2ℓ + 1, (10.6) also holds for j = ℓ, while for j = ℓ and N = 2ℓ we have (2) s ⊕ H (2) c ] ⊗ W (1, ∆ c n;s ) (10.7)…”

Section: Decomposition Of the Tensor Productmentioning

confidence: 99%

“…So far no generally accepted description of this quantum symmetry is available. Accordingly, the analysis of WZW models in the framework of algebraic field theory has been confined to the case of level one of the relevant affine Lie algebras [2,3] or to simple currents [4], i.e. sectors with unit statistical dimension.…”

Section: Introductionmentioning

confidence: 99%

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Higher level WZW sectors from free fermions

Böckenhauer

Fuchs²

1997

Journal of Mathematical Physics

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We introduce a gauge group of internal symmetries of an ambient algebra as a new tool for investigating the superselection structure of WZW theories and the representation theory of the corresponding affine Lie algebras. The relevant ambient algebra arises from the description of these conformal field theories in terms of free fermions. As an illustration we analyze in detail the \son\ WZW theories at level two. In this case there is actually a homomorphism from the representation ring of the gauge group to the WZW fusion ring, even though the level-two observable algebra is smaller than the gauge invariant subalgebra of the field algebra.Comment: LaTeX2e, 30 page

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Section: (96)mentioning

confidence: 99%

Section: Decomposition Of the Tensor Productmentioning

confidence: 99%

Section: Decomposition Of the Tensor Productmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Higher level WZW sectors from free fermions

Böckenhauer

Fuchs²

1997

Journal of Mathematical Physics

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“…We intend to discuss this idea in a subsequent paper. It should be mentioned that Bogoliubov transformations have been successfully used in the construction of localized endomorphisms in conformal field theory models [17,18,19].…”

Section: Introductionmentioning

confidence: 99%

Implementation of Endomorphisms of the Car Algebra

Binnenhei

1995

Rev. Math. Phys.

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The implementation of non-surjective Bogoliubov transformations in Fock states over CAR algebras is investigated. Such a transformation is implementable by a Hilbert space of isometries if and only if the well-known Shale-Stinespring condition is met. In this case, the dimension of the implementing Hilbert space equals the square root of the Watatani index of the associated inclusion of CAR algebras, and both are determined by the Fredholm index of the corresponding one-particle operator. Explicit expressions for the implementing operators are obtained, and the connected components of the semigroup of implementable transformations are described.

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The Physics Superselection Principle in Vertex Operator Algebra Theory

1997

Journal of Algebra

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We formulate an interpretation of the theory of physics superselection sectors in terms of vertex operator algebra language and prove some initial results. As one of the main results we give a construction of simple currents from a weight-one primary semisimple element. By applying our results to vertex operator algebras associated to affine Lie algebras or to positive-definite even lattices, we construct their simple currents.ᮊ 1997 Academic Press

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Level 1 WZW superselection sectors

Cited by 14 publications

References 16 publications

Higher level WZW sectors from free fermions

Higher level WZW sectors from free fermions

Implementation of Endomorphisms of the Car Algebra

The Physics Superselection Principle in Vertex Operator Algebra Theory

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