Simple Current Extensions and Mapping Class Group Representations

Bantay, P.

doi:10.1142/s0217751x9800007x

Cited by 25 publications

(42 citation statements)

References 8 publications

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“…For instance, the quantities ψ λ andψ ρ that appear in the definition (5.9) A of the matrixS are best regarded as elements of the affina of the respective character groups, because [28] the matrices S J are only defined up to certain changes of basis in the space of one-point blocks on the torus and because such a change amounts to a relabelling of the characters.…”

Section: Boundary Homogeneitymentioning

confidence: 99%

Symmetry breaking boundaries

Fuchs

Schweigert

2000

Nuclear Physics B

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Various structural properties of the space of symmetry breaking boundary conditions that preserve an orbifold subalgebra are established. To each such boundary condition we associate its automorphism type. We show that correlation functions in the presence of such boundary conditions are expressible in terms of twisted boundary blocks which obey twisted Ward identities. The subset of boundary conditions that share the same automorphism type is controlled by a classifying algebra, whose structure constants are shown to be traces on spaces of chiral blocks. T-duality on boundary conditions is not a one-to-one map in general. These structures are illustrated in a number of examples. Several applications, including the construction of non-BPS boundary conditions in string theory, are exhibited.

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Section: Boundary Homogeneitymentioning

confidence: 99%

Symmetry breaking boundaries

Fuchs

Schweigert

2000

Nuclear Physics B

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“…This way we have several nice structures at our disposal, which have passed various rather non-trivial checks in chiral conformal field theory (see e.g. [12,13,14,15]). They allow us to write down a natural candidate for a classifying algebra.…”

Section: Introductionmentioning

confidence: 99%

Symmetry breaking boundaries I. General theory

1999

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We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group. We explicitly construct the boundary states and reflection coefficients as well as the annulus amplitudes. Integrality of the annulus coefficients is proven in full generality.Comment: 60 pages, LaTeX2e; typos fixed and other minor correction

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“…As a consequence, for Picard categories the chiral data are particularly well accessible; this is one of the sources of the power of simple current methods in CFT (see e.g. [33,34,18,2]). …”

Section: Picard Groupsmentioning

confidence: 99%

Picard groups in rational conformal field theory

Fröhlich¹,

Fuchs²,

Runkel³

et al. 2005

Noncommutative Geometry and Representation Theory in Mathematical Physics

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Abstract. Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the existence of sets of consistent correlation functions, to demonstrate some of their properties in a model-independent manner, and to derive explicit expressions for OPE coefficients and coefficients of partition functions in terms of invariants of links in three-manifolds. We show that a Morita class of (symmetric special) Frobenius algebras A in a modular tensor category C encodes all data needed to describe the correlators. A Morita-invariant formulation is provided by module categories over C. Together with a bimodule-valued fiber functor, the system (tensor category + module category) can be described by a weak Hopf algebra. The Picard group of the category C can be used to construct examples of symmetric special Frobenius algebras. The Picard group of the category of A-bimodules describes the internal symmetries of the theory and allows one to identify generalized Kramers-Wannier dualities.

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Simple Current Extensions and Mapping Class Group Representations

Abstract: The conjecture of Fuchs, Schellekens and Schweigert on the relation of mapping class group representations and fixed point resolution in simple current extensions is investigated, and a cohomological interpretation of the untwisted stabilizer is given.

Cited by 25 publications

References 8 publications

Symmetry breaking boundaries

Symmetry breaking boundaries

Symmetry breaking boundaries I. General theory

Picard groups in rational conformal field theory

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