Mapping Class Group Representations and Generalized Verlinde Formula

Bantay, P.; Vecsernyés, Péter

doi:10.1142/s0217751x99000683

Cited by 12 publications

(19 citation statements)

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“…Because of this they realise another representation of the usual Verlinde algebra. This formula, which derives from the Moore-Seiberg torus duality identity, appears to have been already considered, following a different motivation, in [72].…”

Section: Relation To the Moore-seiberg Set Of Duality Equationsmentioning

confidence: 99%

Boundary conditions in rational conformal field theories

et al. 2000

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We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph G to each RCFT such that the conformal boundary conditions are labelled by the nodes of G. This approach is carried to completion for s (2) theories leading to complete sets of conformal boundary conditions, their associated cylinder partition functions and the A-D-E classification. We also review the current status for WZW s (3) theories. Finally, a systematic generalization of the formalism of Cardy-Lewellen is developed to allow for multiplicities arising from more general representations of the Verlinde algebra. We obtain information on the bulk-boundary coefficients and reproduce the relevant algebraic structures from the sewing constraints.

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Section: Relation To the Moore-seiberg Set Of Duality Equationsmentioning

confidence: 99%

Boundary conditions in rational conformal field theories

et al. 2000

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“…From the results of [3] we can actually compute explicitly η(p, α), leading to which connect µ(p, α) with φ p (α, β) and η(p, α), while Eq. (54) and the explicit trace formulae of [3] give…”

Section: Simple Current One-point Blocks : the Canonical Basis Choicementioning

confidence: 99%

Simple Current Extensions and Mapping Class Group Representations

Bantay

1998

Int. J. Mod. Phys. A

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“…The general form of Ŝi j was determined e.g. in [66,67]. They are also known to satisfy a generalized version of the Verlinde formula where the summation is over 2 invariant primaries and N j iα is the trace of the 2 action g on the fusion space among i, j and α, see also [46].…”

Section: A Rcfts and Their 2 Symmetriesmentioning

confidence: 99%