The origin of multiplets of chiral fields inSU(2)kat rational level

Nichols, A.

doi:10.1088/1742-5468/2004/09/p09006

Cited by 5 publications

(17 citation statements)

References 57 publications

(108 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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: 60%

“…Also, even thoughÂ 2 does not appear explicitly in some of these expressions, it may nevertheless be related toÂ 1 . For the sake of simplicity, the solutions listed here are merely indicating the general form and the degrees of freedom without reference to the fate of all the various parameters appearing in the ansatz (9). Similar comments also apply to the results on correlators discussed in the following.…”

Section: Two-point Conformal Blocksmentioning

confidence: 88%

“…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: 92%

See 2 more Smart Citations

Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

Rasmussen

2006

Nuclear Physics B

View full text Add to dashboard Cite

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.

show abstract

“…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: 60%

Section: Two-point Conformal Blocksmentioning

confidence: 88%

See 1 more Smart Citation

Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

Rasmussen

2006

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…(4.12)) has been displayed by A. Nichols in [29]. Remark 4.1 We note that the difference of conformal dimensions…”

Section: Proposition 34mentioning

confidence: 80%

“…The field g(x) and the chiral vertex operator u(x) are multivalued functions of monodromy 29) respectively, where M p is diagonal,…”

Section: Monodromy and The Quantum Doublementioning

confidence: 99%

Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral su(2) WZNW Model

2007

View full text Add to dashboard Cite

A zero modes' Fock space F q is constructed for the extended chiral su(2) WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping algebra U q = U q sl(2) at an even root of unity, q h = −1 , and of its infinite dimensional extensionŨ q by the Lusztig operators E (h) , F (h) . We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations of U q . A central result is the characterization of the Grothendieck ring of both U q and U q in Theorem 3.1. The properties of theŨ q fusion ring in F q are related to the braiding properties of correlation functions of primary fields of the conformal su(2) h−2 current algebra model.

show abstract

Toward logarithmic extensions of $$\widehat{s\ell }(2)_k $$ conformal field models

Semikhatov

2007

Theor Math Phys

View full text Add to dashboard Cite

For positive integers p = k + 2, we construct a logarithmic extension of the b s (2) k conformal field theory of integrable representations by taking the kernel of two fermionic screening operators in a butterfly resolution of a three-boson realization of b s (2) k . The currents W − (z) and W + (z) of a W -algebra acting in the kernel are determined by a highest-weight state of dimension 4p − 2 and charge 2p − 1 and by a (θ=1)-twisted highest-weight state of the same dimension 4p−2 and opposite charge −2p+1. We construct 2p W -algebra representations, evaluate their characters, and show that together with the p−1 integrable representation characters, they generate a modular group representation whose structure is described as a deformation ofs (2) k integrable-representation characters and Rp+1 is a (p+1)-dimensional SL(2, Z)-representation known from the logarithmic (p, 1) model. The dimension 9p − 3 is conjecturally the dimension of the space of torus amplitudes, and the C n with n = 2 and 3 suggest the Jordan cell sizes in indecomposable W -algebra modules. We show that under Hamiltonian reduction, the W -algebra currents map into the currents of the triplet W -algebra of the logarithmic (p, 1) model.

show abstract

The origin of multiplets of chiral fields inSU(2)_kat rational level

Cited by 5 publications

References 57 publications

Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral su(2) WZNW Model

Toward logarithmic extensions of $$\widehat{s\ell }(2)_k $$ conformal field models

Contact Info

Product

Resources

About