The WZW model and the βγ system

Lesage, Frédéric; Mathieu, Pierre; Rasmussen, Jørgen; Saleur, Hubert

doi:10.1016/s0550-3213(02)00905-7

Cited by 63 publications

(124 citation statements)

References 47 publications

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“…Alternative extensions have appeared in the literature, see [6,7,8,4,9], for example, but all seem to differ significantly from ours in foundation and approach.…”

Section: Introductionmentioning

confidence: 62%

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Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

Rasmussen

2006

Nuclear Physics B

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We study a particular type of logarithmic extension of SL(2, R) Wess-Zumino-Witten models. It is based on the introduction of affine Jordan cells constructed as multiplets of quasi-primary fields organized in indecomposable representations of the Lie algebra sl(2). We solve the simultaneously imposed set of conformal and SL(2, R) Ward identities for two-and three-point chiral blocks. These correlators will in general involve logarithmic terms and may be represented compactly by considering spins with nilpotent parts. The chiral blocks are found to exhibit hierarchical structures revealed by computing derivatives with respect to the spins. We modify the Knizhnik-Zamolodchikov equations to cover affine Jordan cells and show that our chiral blocks satisfy these equations. It is also demonstrated that a simple and well-established prescription for hamiltonian reduction at the level of ordinary correlators extends straightforwardly to the logarithmic correlators as the latter then reduce to the known results for twoand three-point conformal blocks in logarithmic conformal field theory.

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“…Alternative extensions have appeared in the literature, see [6,7,8,4,9], for example, but all seem to differ significantly from ours in foundation and approach.…”

Section: Introductionmentioning

confidence: 62%

“…This is illustrated by the models discussed in [6,7,8,4,9], for example, and will be addressed further elsewhere. The construction developed in the present work has the virtue that it, under hamiltonian reduction, reduces to the non-affine logarithmic CFT reviewed in Section 2.…”

Section: More On Indecomposable Sl(2) Representationsmentioning

confidence: 93%

Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

Rasmussen

2006

Nuclear Physics B

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“…Since Ω ⊗ Ω ∈ N , we have N = 0 in the quotient space H bulk , and a correlator involving an insertion of N has to vanish. In particular, 0 = µ(x+iy) N(iy) 34) which implies that C 1 = 0, independent of the choice of boundary condition b. Similarly, we have 35) where in the last step we used that C 1 = 0.…”

Section: One µ and One ω Field On The Upper Half Planementioning

confidence: 99%

“…Logarithmic vertex operator algebras have finally attracted some attention in mathematics [27,28,29]. Most work has been done on the c = −2 triplet theory, but logarithmic conformal field theories have also appeared in other contexts, in particular for theories with super group symmetries, see for example [2,13,30,31], as well as in other classes of models, for example [32,33,34,35].…”

Section: Introductionmentioning

confidence: 99%

The logarithmic triplet theory with boundary

Gaberdiel¹,

Runkel²

2006

J. Phys. A: Math. Gen.

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The boundary theory for the c = −2 triplet model is investigated in detail. In particular, we show that there are four different boundary conditions that preserve the triplet algebra, and check the consistency of the corresponding boundary operators by constructing their OPE coefficients explicitly. We also compute the correlation functions of two bulk fields in the presence of a boundary, and verify that they are consistent with factorisation.

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“…In the case of fixed boundary conditions, instead,R AĀ (θ) = −1 and the short distance limit is easily derived 8 The resolution of the identity explicitly reads…”

Section: ω Operatormentioning

confidence: 99%

Massive ghost theories with a line of defects

Mosconi¹

2003

J. Phys. A: Math. Gen.

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We study free massive fermionic ghosts, in the presence of an extended line of impurities. The corresponding scattering theory can be formulated by adding to the bulk S-matrix the scattering amplitudes, describing the interactions among the bulk excitations and the defect line (transmission and reflection amplitudes). Explicit expressions for such matrices can be found by solving a bootstrap system of equations (unitarity, crossing and factorization) or, alternatively, relying on a Lagrangian description in terms of Symplectic fermions. In this framework, two distinct defect interactions are proposed (a relevant and a marginal ones), and exact expressions for the correlation functions of the most significant operators in the theory are derived, exploiting the bulk form factors and the matrix elements relative to the defect operator, encoding the entire information about the inhomogeneities.

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The WZW model and the βγ system

Cited by 63 publications

References 47 publications

Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

The logarithmic triplet theory with boundary

Massive ghost theories with a line of defects

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