TY - JOUR

T1 - Twisted boundary states and representation of generalized fusion algebra

AU - Ishikawa, Hiroshi

AU - Tani, Taro

N1 - Copyright:
Copyright 2006 Elsevier B.V., All rights reserved.

PY - 2006/4/10

Y1 - 2006/4/10

N2 - 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 ≅ S3. Finally, we give an argument that the graph fusion algebra associated with simple current 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.

AB - 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 ≅ S3. Finally, we give an argument that the graph fusion algebra associated with simple current 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.

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U2 - 10.1016/j.nuclphysb.2006.01.031

DO - 10.1016/j.nuclphysb.2006.01.031

M3 - Article

AN - SCOPUS:33644603210

VL - 739

SP - 328

EP - 388

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -