Logarithmic conformal field theory through nilpotent conformal dimensions

Moghimi-Araghi, S.; Rouhani, S.; Saadat, Mozafar

doi:10.1016/s0550-3213(01)00004-9

Cited by 34 publications

(56 citation statements)

References 19 publications

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“…We will follow this idea here, though use an approach closer to the one employed in [17,18,13]. We thus define the field or unified cell…”

Section: Conformal Jordan Cellmentioning

confidence: 99%

“…By consideringθ i as the nilpotent part of the generalized conformal weight∆ i +θ i [17,13], one may represent the results (11) as…”

Section: Two-point Conformal Blocksmentioning

confidence: 99%

“…Here we wish to extend to the logarithmic WZW model the idea put forward in [17] that correlators in logarithmic CFT may be represented compactly by considering conformal weights with nilpotent partŝ ∆ +θ. The most general results of this kind for two-and three-point conformal blocks were found in [13] and are given above as (13) and (18).…”

Section: In Terms Of Spins With Nilpotent Partsmentioning

confidence: 99%

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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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“…We will follow this idea here, though use an approach closer to the one employed in [17,18,13]. We thus define the field or unified cell…”

Section: Conformal Jordan Cellmentioning

confidence: 99%

“…By consideringθ i as the nilpotent part of the generalized conformal weight∆ i +θ i [17,13], one may represent the results (11) as…”

Section: Two-point Conformal Blocksmentioning

confidence: 99%

Section: In Terms Of Spins With Nilpotent Partsmentioning

confidence: 99%

See 1 more Smart Citation

Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

Rasmussen

2006

Nuclear Physics B

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“…We will follow this idea here, though use an approach closer to the one employed in [5,9]. We thus define the field or unified…”

Section: Correlators In Logarithmic Conformal Field Theorymentioning

confidence: 99%

On logarithmic solutions to the conformal Ward identities

Rasmussen¹

2005

Nuclear Physics B

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A general discussion of the conformal Ward identities is presented in the context of logarithmic conformal field theory with conformal Jordan cells of rank two. The logarithmic fields are taken to be quasi-primary. No simplifying assumptions are made about the operator-product expansions of the primary or logarithmic fields. Based on a very natural and general ansatz about the form of the two-and three-point functions, their complete solutions are worked out. The results are in accordance with and extend the known results. It is demonstrated, for example, that the correlators exhibit hierarchical structures similar to the ones found in the literature pertaining to certain simplifying assumptions.

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“…All this procedure may be redone using the nilpotent variables [80], directly deriving the correlators using the non-relativistic algebra. 5 We are also able to consider a Jordan cell structure for the rapidity:…”

Section: Conformal Galilean Algebramentioning

confidence: 99%

Logarithmic correlators or responses in non-relativistic analogues of conformal invariance

Henkel¹,

Rouhani²

2013

J. Phys. A: Math. Theor.

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Recent developments on emergence of logarithmic terms in correlators or response functions of models which exhibit dynamical symmetries analogous to conformal invariance in not necessarily relativistic systems are reviewed. The main examples of these are logarithmic Schrödinger-invariance and logarithmic conformal Galilean invariance. Some applications of these ideas to statistical physics are described.

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Logarithmic conformal field theory through nilpotent conformal dimensions

Cited by 34 publications

References 19 publications

Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

On logarithmic solutions to the conformal Ward identities

Logarithmic correlators or responses in non-relativistic analogues of conformal invariance

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