Logarithmic extensions of minimal models: Characters and modular transformations

Feigin, Boris; Gainutdinov, Azat M.; Semikhatov, A. M.; Tipunin, I. Yu.

doi:10.1016/j.nuclphysb.2006.09.019

Cited by 167 publications

(356 citation statements)

References 45 publications

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“…Infinitely many logCFTs were later constructed by extending the Kac table of the ordinary Virasoro minimal models [18]. Both the representation content and the fusion rules of these "logarithmic minimal models" have been studied in detail [19][20][21][22][23]. A partially overlapping direction of research has focused on realizing 2d logCFTs as continuum limits of lattice models, see for instance [24][25][26][27].…”

Section: Jhep10(2017)201mentioning

confidence: 99%

The ABC (in any D) of logarithmic CFT

Hogervorst

Paulos

Vichi

2017

J. High Energ. Phys.

103

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Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our analysis is modelindependent and holds for any spacetime dimension. Our results include a determination of the general form of correlation functions and conformal block decompositions, clearing the path for future bootstrap applications. Several examples are discussed in detail, including logarithmic generalized free fields, holographic models, self-avoiding random walks and critical percolation.

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Section: Jhep10(2017)201mentioning

confidence: 99%

The ABC (in any D) of logarithmic CFT

Hogervorst

Paulos

Vichi

2017

J. High Energ. Phys.

103

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“…Their role for logarithmic extensions of minimal models was also emphasized in [76,78], mostly based on studies of the dual quantum group. It seems worth pointing out, though, that for quotients of supergroups, projective modules might not play such a prominent role, even though some of them are likely to be logarithmic as well.…”

Section: Jhep09(2007)085mentioning

confidence: 99%

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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“…But given a q i,i = −1 and trying to reconstruct a screening in general leads to the condition 3 Recall that rational conformal field theories are generally defined as the cohomology of a complex associated with the screenings, whereas logarithmic models are defined by the kernel (cf. [18,27,28,29]). In particular, this allows interesting logarithmic conformal models to exist in the cases where the rational model is nonexistent (the (p, 1) series) or trivial (the (2, 3) model).…”

Section: Points To Notementioning

confidence: 99%

“…The corresponding CFT model is the product (p ′ , 1) × (1, p)) of two "(p, 1)" models [27,30], or, in the degenerate case where α and β are collinear (and hence only one boson is needed), the (p ′ , p) model [28,31].…”

Section: The List Itemmentioning

confidence: 99%

Virasoro Central Charges for Nichols Algebras

Semikhatov

2014

Mathematical Lectures From Peking University

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ABSTRACT. A Virasoro central charge can be associated with each Nichols algebra with diagonal braiding in a way that is invariant under the Weyl groupoid action. The central charge takes very suggestive values for some items in Heckenberger's list of rank-2 Nichols algebras. In particular, this might be viewed as an indication of the existence of reasonable logarithmic extensions of W 3 ≡ WA 2 , WB 2 , and WG 2 models of conformal field theory. In the W 3 case, the construction of an octuplet extended algebra-a counterpart of the triplet (1, p) algebra-is outlined.

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Logarithmic extensions of minimal models: Characters and modular transformations

Cited by 167 publications

References 45 publications

The ABC (in any D) of logarithmic CFT

The ABC (in any D) of logarithmic CFT

Free fermion resolution of supergroup WZNW models

Virasoro Central Charges for Nichols Algebras

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