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Ishikawa, H; Tani, T; Ishikawa, H , Tohoku Univ, Dept Phys, Sendai, Miyagi 9808578, Japan
Twisted boundary states and representation of generalized fusion algebra
Source PublicationNUCLEAR PHYSICS B
KeywordConformal Field-theories Symmetry-breaking Boundaries Virasoro Minimal Models Modular Invariants Alpha-induction Structure Constants Graphs Subfactors Nets Operators
AbstractThe mutual consistency of boundary conditions twisted by an automorphism group G of the chiral algebra is studied for general modular invariants of rational conformal field theories. We show that a consistent set of twisted boundary states associated with any modular invariant realizes a non-negative integer matrix representation (NIM-rep) of the generalized fusion algebra, an extension of the fusion algebra by representations of the twisted chiral algebra associated with the automorphism group G. We check this result for several concrete cases. In particular, we find that two NIM-reps of the fusion algebra for su(3)(k) (k = 3, 5) are organized into a NIM-rep of the generalized fusion algebra for the charge-conjugation automorphism of su(3)k. We point out that the generalized fusion algebra is non-commutative if G is non-Abelian and provide some examples for G congruent to S-3. Finally, we give an argument that the graph fusion algebra associated with simple cut-rent extensions coincides with the generalized fusion algebra for the extended chiral algebra, and thereby explain that the graph fusion algebra contains the fusion algebra of the extended theory as a subalgebra. (c) 2006 Elsevier B.V. All rights reserved.
2006
ISSN0550-3213
Volume739Issue:3Pages:328-388
Subject AreaPhysics
Indexed BySCI
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Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/6004
Collection理论物理所科研产出_SCI论文
Corresponding AuthorIshikawa, H , Tohoku Univ, Dept Phys, Sendai, Miyagi 9808578, Japan
Recommended Citation
GB/T 7714
Ishikawa, H,Tani, T,Ishikawa, H , Tohoku Univ, Dept Phys, Sendai, Miyagi 9808578, Japan. Twisted boundary states and representation of generalized fusion algebra[J]. NUCLEAR PHYSICS B,2006,739(3):328-388.
APA Ishikawa, H,Tani, T,&Ishikawa, H , Tohoku Univ, Dept Phys, Sendai, Miyagi 9808578, Japan.(2006).Twisted boundary states and representation of generalized fusion algebra.NUCLEAR PHYSICS B,739(3),328-388.
MLA Ishikawa, H,et al."Twisted boundary states and representation of generalized fusion algebra".NUCLEAR PHYSICS B 739.3(2006):328-388.
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