Fusion Rules for Extended Current Algebras

Baver, Ernest; Gepner, Doron

doi:10.1142/s0217732396001934

Cited by 14 publications

(44 citation statements)

References 13 publications

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“…The SU (3) 1 positive energy representations obey Z 3 fusion rules, and from ασ-reciprocity we conclude that the marked vertices are given by Figure 10: D (6) (Clearly we have the freedom to define which is [α (1) 2 ] and which [α…”

Section: More Examplesmentioning

confidence: 95%

“…The homomorphism property of α-induction also implies that V carries a representation of W which therefore decomposes into a direct sum over the characters γ Λ of the fusion algebra W which are labelled by admissible weights Λ as well. The representation matrix associated to the first fundamental weight Λ (1) can be interpreted as the adjacency matrix of a graph (which is in fact the fusion graph of α Λ (1) ), and its eigenvalues are the evaluation of the characters γ Λ in the decomposition of this representation of W . The weights Λ labelling the characters which in fact appear this way are called exponents as can be recognized as a generalization of the Coxeter exponents in the SU (2) case.…”

Section: Outline Of This Papermentioning

confidence: 99%

“…Thus the sectors [λ (p,q) ] constitute the sector basis of the fusion algebra W (3, k). Recall that the the fusion of the sector [λ (1,0) ] that corresponds to the fundamental representation is…”

Section: More Examplesmentioning

confidence: 99%

“…For SU (2) and SU (3) both cases actually exhaust all the block-diagonal modular invariants. 1 The modular invariants appear to be labelled naturally, in the case of In the subfactor theory only A-D-E Dynkin diagrams with A ℓ+1 , D 2ℓ+2 (ℓ = 1, 2, ...), E 6 and E 8 , appear as the (dual) principal graphs (or fusion graphs) of subfactors with index less than four. In the rational conformal field theory of SU (2) models described by A-D-E Dynkin diagrams, one may argue that there is a degeneracy so that only D even , E 6 and E 8 , namely the type I cases need be counted.…”

Section: Introductionmentioning

confidence: 99%

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

Böckenhauer

Evans

1999

Communications in Mathematical Physics

107

440

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We apply the theory of α-induction of sectors which we elaborated in our previous paper to several nets of subfactors arising from conformal field theory. The main application are conformal embeddings and orbifold inclusions of SU (n) WZW models. For the latter, we construct the extended net of factors by hand. Developing further some ideas of F. Xu, our treatment leads canonically to certain fusion graphs, and in all our examples we rediscover the graphs Di Francesco, Petkova and Zuber associated empirically to the corresponding SU (n) modular invariants. We establish a connection between exponents of these graphs and the appearance of characters in the block-diagonal modular invariants, provided that the extended modular S-matrices diagonalize the endomorphism fusion rules of the extended theories. This is proven for many cases, and our results cover all the block-diagonal SU (2) modular invariants, thus provide some explanation of the A-D-E classification.

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Section: More Examplesmentioning

confidence: 95%

Section: Outline Of This Papermentioning

confidence: 99%

Section: More Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Böckenhauer

Evans

1999

Communications in Mathematical Physics

107

440

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“…Many such expressions for characters of conformal field theories are known already, for example, [5,6,7,8,9].…”

mentioning

confidence: 99%

Generalized Rogers Ramanujan Identities Motivated by AGT Correspondence

Belavin

Gepner

2013

Lett Math Phys

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AGT correspondence and its generalizations attracted a great deal of attention recently. In particular it was suggested that U (r) instantons on R 4 /Z p describe the conformal blocks of the coset A(r,where n is a parameter. Our purpose here is to describe Generalized Rogers Ramanujan (GRR) identities for these cosets, which expresses the characters as certain q series. We propose that such identities exist for the coset A(r, p) for all positive integers n and all r and p. We treat here the case of n = 1 and r = 2, finding GRR identities for all the characters.

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Fusion of Symmetric D-Branes and Verlinde Rings

Carey

Wang

2007

Commun. Math. Phys.

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We explain how multiplicative bundle gerbes over a compact, connected and simple Lie group G lead to a certain fusion category of equivariant bundle gerbe modules given by pre-quantizable Hamiltonian LG-manifolds arising from Alekseev-Malkin-Meinrenken's quasi-Hamiltonian G-spaces. The motivation comes from string theory namely, by generalising the notion of D-branes in G to allow subsets of G that are the image of a G-valued moment map we can define a 'fusion of D-branes' and a map to the Verlinde ring of the loop group of G which preserves the product structure. The idea is suggested by the theorem of Freed-Hopkins-Teleman. The case where G is not simply connected is studied carefully in terms of equivariant bundle gerbe modules for multiplicative bundle gerbes.

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Fusion Rules for Extended Current Algebras

Cited by 14 publications

References 13 publications

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

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

Generalized Rogers Ramanujan Identities Motivated by AGT Correspondence

Fusion of Symmetric D-Branes and Verlinde Rings

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