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  • 1
    Electronic Resource
    Electronic Resource
    Some symmetries of quantum dimensions (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1770-1775 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Several useful properties of the quantum dimensions of representations of Uq(sl(n)) for q a root of unity are established. The results can be used to calculate truncated Kronecker products of these representations and hence to investigate the isomorphism between these truncated tensor products and the fusion rules of the WZW theories associated with Uq(sl(n)).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528673
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  • 2
    Electronic Resource
    Electronic Resource
    Physical state conditions and supersymmetry breaking in quantum mechanics (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 349-353 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown, by giving an explicit example, how the conditions imposed on physically admissible states can affect the pattern of supersymmetry breaking and, as a consequence, the values of physically interesting quantities such as the Witten index. As a by-product an unusual kind of explicit supersymmetry breaking is observed, where the supersymmetry algebra still holds formally, as well as a spontaneous breakdown of supersymmetry, which is not induced by instantons.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527339
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  • 3
    Electronic Resource
    Electronic Resource
    Simple WZW currents (1991)
    Springer
    Communications in mathematical physics 136 (1991), S. 345-356 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A complete classification of simple currents of WZW theories is obtained. The proof is based on an analysis of the quantum dimensions of the primary fields. Simple currents are precisely the primaries with unit quantum dimension; for WZW theories explicit formulae for the quantum dimensions can be derived so that an identification of the fields with unit quantum dimension is possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02100029
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  • 4
    Electronic Resource
    Electronic Resource
    Level 1 WZW superselection sectors (1992)
    Springer
    Communications in mathematical physics 146 (1992), S. 553-583 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The superselection structure of the Wess-Zumino-Witten theory based on the affine Lie algebra $$\widehat{so}(N)$$ at level one is investigated for arbitraryN. By making use of the free fermion representation of the affine algebra, the endomorphisms which represent the superselection sectors on the observable algebra can be constructed as endomorphisms of the underlying Majorana algebra. These endomorphisms do not close on the chiral algebra of the theory, but we are able to obtain a larger algebra on which the endomorphisms close. The composition of equivalence classes of the endomorphisms reproduces the WZW fusion rules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02097016
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  • 5
    Electronic Resource
    Electronic Resource
    The Action of Outer Automorphisms on Bundles¶of Chiral Blocks (1999)
    Springer
    Communications in mathematical physics 206 (1999), S. 691-736 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the Knizhnik–Zamolodchikov connection and have finite order. When all primary fields are fixed points, the isomorphisms are endomorphisms; in this case, the bundle of chiral blocks is typically a reducible vector bundle. A conjecture for the trace of such endomorphisms is presented; the proposed relation generalizes the Verlinde formula. Our results have applications to conformal field theories based on non-simply connected groups and to the classification of boundary conditions in such theories.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050841
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  • 6
    Electronic Resource
    Electronic Resource
    Quasi-Galois symmetries of the modularS-matrix (1996)
    Springer
    Communications in mathematical physics 176 (1996), S. 447-465 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The recently introduced Galois symmetries of rational conformal field theory are generalized, for the case of WZW theories, to “quasi-Galois symmetries.” These symmetries can be used to derive a large number of equalities and sum rules for entries of the modular matrixS, including some that previously had been observed empirically. In addition, quasi-Galois symmetries allow us to construct modular invariants and to relateS-matrices as well as modular invariants at different levels. They also lead us to a convenient closed expression for the branching rules of the conformal embeddings .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099557
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  • 7
    Electronic Resource
    Electronic Resource
    WZW Fusion Rings in the Limit of Infinite Level (1997)
    Springer
    Communications in mathematical physics 185 (1997), S. 641-670 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We show that the WZW fusion rings at finite levels form a projective system with respect to the partial ordering provided by divisibility of the height, i.e. the level shifted by a constant. From this projective system we obtain WZW fusion rings in the limit of infinite level. This projective limit constitutes a mathematically well-defined prescription for the “classical limit” of WZW theories which replaces the naive idea of “sending the level to infinity.” The projective limit can be endowed with a natural topology, which plays an important rôle for studying its structure. The representation theory of the limit can be worked out by considering the associated fusion algebra; this way we obtain in particular an analogue of the Verlinde formula.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050104
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  • 8
    Electronic Resource
    Electronic Resource
    From Dynkin diagram symmetries to fixed point structures (1996)
    Springer
    Communications in mathematical physics 180 (1996), S. 39-97 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra g induces an automorphism of g and a mappingτ ω between highest weight modules of g. For a large class of such Dynkin diagram automorphisms, we can describe various aspects of these maps in terms of another Kac-Moody algebra, the “orbit Lie algebra” ğ. In particular, the generating function for the trace ofτ ω over weight spaces, which we call the “twining character” of g (with respect to the automorphism), is equal to a character of ğ. The orbit Lie algebras of untwisted affine Lie algebras turn out to be closely related to the fixed point theories that have been introduced in conformal field theory. Orbit Lie algebras and twining characters constitute a crucial step towards solving the fixed point resolution problem in conformal field theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02101182
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  • 9
    Electronic Resource
    Electronic Resource
    Simple WZW superselection sectors (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 31-41 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 17B37 ; 81T05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The superselection structure of simple currents of chiral Wess-Zumino-Witten theories, at arbitrary valuek ∈ ℕ of the corresponding affine Lie algebra, is described in terms of explicit localizable automorphisms of the affine algebra. These automorphisms are induced by certain Dynkin diagram automorphisms; under composition, they form an Abelian group isomorphic to the center of the relevant simply connected simple Lie group and, hence, reproduce the WZW fusion rules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739564
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  • 10
    Electronic Resource
    Electronic Resource
    Fusion rule engineering (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 11-18 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 16Dxx ; 81T
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The determination of the fusion rules of WZW theories constitutes an important step in the program of classifying and solving conformal field theories. A drawback of the existing algorithms for such calculations is that, even at a modestly large number of primary fields, they require an enormous amount of computer time and memory. However, by breeding together two of these algorithms in an appropriate manner, it is possible to speed up the calculations and, therefore, greatly extend the accessible range of theories.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01811289
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