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36
Category theory for conformal boundary conditions
 FIELDS INST. COMMUN. AMER. MATH. SOC., PROVIDENCE, RI
, 2003
"... ... inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As a byproduct we obtain results about the FrobeniusSchur indicator in sovereign tensor categories. A braiding on C is not needed, nor is semisimplicity. We apply our results to the d ..."
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Cited by 50 (14 self)
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... inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As a byproduct we obtain results about the FrobeniusSchur indicator in sovereign tensor categories. A braiding on C is not needed, nor is semisimplicity. We apply our results to the description of boundary conditions in twodimensional conformal field theory and present illustrative examples. We show that when the module category is tensor, then it gives rise to a NIMrep of the fusion rules, and discuss a possible relation with the representation theory of vertex operator algebras.
TFT CONSTRUCTION OF RCFT CORRELATORS V: PROOF OF MODULAR INVARIANCE AND FACTORISATION
, 2006
"... The correlators of twodimensional rational conformal field theories that are obtained in the TFT construction of [FRS I, FRS II, FRS IV] are shown to be invariant under ..."
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Cited by 32 (19 self)
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The correlators of twodimensional rational conformal field theories that are obtained in the TFT construction of [FRS I, FRS II, FRS IV] are shown to be invariant under
TFT CONSTRUCTION OF RCFT CORRELATORS IV: STRUCTURE CONSTANTS AND CORRELATION FUNCTIONS
, 2005
"... We compute the fundamental correlation functions in twodimensional rational conformal field theory, from which all other correlators can be obtained by sewing: the correlators of three bulk fields on the sphere, one bulk and one boundary field on the disk, three boundary fields on the disk, and one ..."
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Cited by 28 (13 self)
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We compute the fundamental correlation functions in twodimensional rational conformal field theory, from which all other correlators can be obtained by sewing: the correlators of three bulk fields on the sphere, one bulk and one boundary field on the disk, three boundary fields on the disk, and one bulk field on the cross cap. We also consider conformal defects and calculate the correlators of three defect fields on the sphere and of one defect field on the cross cap. Each of these correlators is presented as the product of a structure constant and the appropriate conformal two or threepoint block. The structure constants are expressed as invariants of ribbon graphs in threemanifolds.
TFT construction of RCFT correlators III: Simple currents
 Nucl. Phys. B
"... We use simple currents to construct symmetric special Frobenius algebras in modular tensor categories. We classify such simple current type algebras with the help of abelian group cohomology. We show that they lead to the modular invariant torus partition functions that have been studied by Kreuzer ..."
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Cited by 22 (10 self)
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We use simple currents to construct symmetric special Frobenius algebras in modular tensor categories. We classify such simple current type algebras with the help of abelian group cohomology. We show that they lead to the modular invariant torus partition functions that have been studied by Kreuzer and Schellekens. We also classify boundary conditions in the associated conformal field theories and show that the boundary states are given by the formula proposed in hepth/0007174. Finally, we investigate conformal defects in these
Duality and defects in rational conformal field theory
, 2006
"... We study topological defect lines in twodimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects separating different phases of local CFTs with the same chiral symmetry are included in our discussion. We sh ..."
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Cited by 20 (7 self)
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We study topological defect lines in twodimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects separating different phases of local CFTs with the same chiral symmetry are included in our discussion. We show how the resulting onedimensional phase boundaries can be used to extract symmetries and orderdisorder dualities of the CFT. The case of central charge c = 4/5, for which there are two inequivalent world sheet phases corresponding to the tetracritical Ising model and the critical threestates
Boundary States in c = −2 Logarithmic Conformal Field Theory
, 2002
"... Starting from first principles, a constructive method is presented to obtain boundary states in conformal field theory. It is demonstrated that this method is well suited to compute the boundary states of logarithmic conformal field theories. By studying the logarithmic conformal field theory with c ..."
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Cited by 13 (3 self)
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Starting from first principles, a constructive method is presented to obtain boundary states in conformal field theory. It is demonstrated that this method is well suited to compute the boundary states of logarithmic conformal field theories. By studying the logarithmic conformal field theory with central charge c = −2 in detail, we show that our method leads to consistent results. In particular, it allows to define boundary states corresponding to both, indecomposable representations as well as their irreducible subrepresentations.
Correspondences of ribbon categories
, 2006
"... Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not have a substantial counterpart for symmetric tensor categories ..."
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Cited by 13 (3 self)
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Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not have a substantial counterpart for symmetric tensor categories. In particular, we exhibit various equivalences involving categories of modules over algebras in ribbon categories. Finally we establish a correspondence of ribbon categories that can be applied to, and is in fact motivated by, the coset construction in conformal quantum field theory.
Full field algebra
 HKo3] [HKr] [HL1] [HL2] [HL3] [HL4] [HL5] [K1] Y.Z. Huang and
"... We introduce the notions of openclosed field algebra and openclosed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an openclosed field algebra over V canonically gives an algebra over a Cextension of Swiss ..."
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Cited by 11 (1 self)
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We introduce the notions of openclosed field algebra and openclosed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an openclosed field algebra over V canonically gives an algebra over a Cextension of Swisscheese partial operad. We also give a tensorcategorical formulation and constructions of openclosed field algebras over V. 0
Perturbed defects and Tsystems in conformal field theory
 J. Phys. A
"... Defect lines in conformal field theory can be perturbed by chiral defect fields. If the unperturbed defects satisfy su(2)type fusion rules, the operators associated to the perturbed defects are shown to obey functional relations known from the study of integrable models as Tsystems. The procedure ..."
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Cited by 6 (1 self)
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Defect lines in conformal field theory can be perturbed by chiral defect fields. If the unperturbed defects satisfy su(2)type fusion rules, the operators associated to the perturbed defects are shown to obey functional relations known from the study of integrable models as Tsystems. The procedure is illustrated for Virasoro minimal models and for Liouville theory. Dedicated to the memory of Alexei Zamolodchikov.