An Algebraic Approach to Logarithmic Conformal Field Theory

Gaberdiel, Matthias R.

doi:10.1142/s0217751x03016860

Cited by 195 publications

(264 citation statements)

References 74 publications

(179 reference statements)

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“…While irreducible representations and their projective covers are certainly central objects for all Lie superalgebras, some of their properties may differ considerably from what we have seen in the case of type I. We have 29 Using the analogy to the Kazhdan-Lusztig dual quantum group, they have been called Verma modules in [71].…”

Section: Jhep09(2007)085mentioning

confidence: 99%

“…While (ii) is common to all σ-models, the symmetries of WZNW models are necessary to lift geometric insights to the full field theory. Both aspects single out supergroup WZNW theories among most of the logarithmic conformal field theories that have been considered in the past [27,11,28] (see also [29,30] for reviews and further 1 In contrast to some appearances in the physics literature we will use the word "indecomposable" strictly in the mathematical sense. According to that definition also irreducible representations are always indecomposable since they cannot be written as a direct sum of two other (non-zero) representations.…”

Section: Introductionmentioning

confidence: 99%

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Free fermion resolution of supergroup WZNW models

Quella

Schomerus²

2007

J. High Energy Phys.

132

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Extending our earlier work on PSL(2|2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M |N ) along with several close relatives such as PSL(N |N ), certain Poincaré supergroups and the series OSP (2|2N ). The technical foundation for this remarkable progress is a special Feigin-Fuchs type representation which allows to keep the bosonic symmetry manifest instead of reducing it to free fields. In preparation for the field theory analysis, we shall exploit a minisuperspace analogue of the resulting free fermion construction to deduce the spectrum of the Laplacian on type I supergroups. The latter is shown to be non-diagonalizable. After lifting these results to the full WZNW model, we address various issues of the field theory, including its modular invariance and the computation of correlation functions. In agreement with previous findings, supergroup WZNW models allow to study chiral and non-chiral aspects of logarithmic conformal field theory within a geometric framework. We shall briefly indicate how insights from WZNW models carry over to non-geometric examples, such as e.g. the W(p) triplet models.

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Section: Jhep09(2007)085mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free fermion resolution of supergroup WZNW models

Quella

Schomerus²

2007

J. High Energy Phys.

132

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“…Nonsemisimple fusion algebras are expected to arise in logarithmic models of conformal field theory [7,8,9,10,11,12,13,14,15], where irreducible representations of the chiral algebra allow nontrivial (indecomposable) extensions. In what follows, we generalize the Verlinde formula and derive nonsemisimple fusion algebras for the series of (1, p) Virasoro models with integer p ≥ 2.…”

Section: Introductionmentioning

confidence: 99%

Nonsemisimple Fusion Algebras and the Verlinde Formula

Fuchs

Hwang

Semikhatov

et al. 2004

Communications in Mathematical Physics

129

285

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“…A great deal of effort has been made to characterize and classify abstractly such theories [12,13]. It is fair to say, however, that very few explicit examples are well understood.…”

Section: Introductionmentioning

confidence: 99%

“…It is fair to say, however, that very few explicit examples are well understood. The case of c = −2 has given rise to surprisingly complicated results (see [12,13] for a review), while for potentially more interesting physical theories (such as sigma models on superprojective spaces), partial results reveal a truly baffling complexity [14].…”

Section: Introductionmentioning

confidence: 99%

The WZW model and the βγ system

et al. 2002

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The bosonic βγ ghost system has long been used in formal constructions of conformal field theory. It has become important in its own right in the last few years, as a building block of field theory approaches to disordered systems, and as a simple representative -due in part to its underlying su(2) −1/2 structure -of non-unitary conformal field theories. We provide in this paper the first complete, physical, analysis of this βγ system, and uncover a number of striking features. We show in particular that the spectrum involves an infinite number of fields with arbitrarily large negative dimensions. These fields have their origin in a twisted sector of the theory, and have a direct relationship with spectrally flowed representations in the underlying su(2) −1/2 theory. We discuss the spectral flow in the context of the operator algebra and fusion rules, and provide a re-interpretation of the modular invariant consistent with the spectrum.

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An Algebraic Approach to Logarithmic Conformal Field Theory

Cited by 195 publications

References 74 publications

Free fermion resolution of supergroup WZNW models

Free fermion resolution of supergroup WZNW models

Nonsemisimple Fusion Algebras and the Verlinde Formula

The WZW model and the βγ system

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