Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction

Rasmussen, J. (2006) Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction. Nuclear Physics B, 736 3: 225-258. doi:10.1016/j.nuclphysb.2005.12.009


Author Rasmussen, J.
Title Affine Jordan cells, logarithmic correlators, and Hamiltonian reduction
Journal name Nuclear Physics B   Check publisher's open access policy
ISSN 0550-3213
1873-1562
Publication date 2006-02
Sub-type Article (original research)
DOI 10.1016/j.nuclphysb.2005.12.009
Open Access Status DOI
Volume 736
Issue 3
Start page 225
End page 258
Total pages 34
Place of publication Amsterdam, The Netherlands
Publisher Elsevier
Language eng
Formatted abstract
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 two- and three-point conformal blocks in logarithmic conformal field theory.
Keyword logarithmic conformal field theory
Jordan cell
Wess-Zumino-Witten model
Knizhnik-Zamolodchikov equations
Hamiltonian reduction
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Wed, 21 Mar 2012, 12:18:07 EST by Kay Mackie on behalf of School of Mathematics & Physics