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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 Publication | NUCLEAR PHYSICS B |
Keyword | Conformal Field-theories Symmetry-breaking Boundaries Virasoro Minimal Models Modular Invariants Alpha-induction Structure Constants Graphs Subfactors Nets Operators |
Abstract | The 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 | |
ISSN | 0550-3213 |
Volume | 739Issue:3Pages:328-388 |
Subject Area | Physics |
Indexed By | SCI |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.itp.ac.cn/handle/311006/6004 |
Collection | 理论物理所科研产出_SCI论文 |
Corresponding Author | Ishikawa, 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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