Free field realizations of 2D current algebras, screening currents and primary fields

Petersen, J. L., Rasmussen, J. and Yu, M. (1997) Free field realizations of 2D current algebras, screening currents and primary fields. Nuclear Physics B, 502 3: 649-670.

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Author Petersen, J. L.
Rasmussen, J.
Yu, M.
Title Free field realizations of 2D current algebras, screening currents and primary fields
Journal name Nuclear Physics B   Check publisher's open access policy
ISSN 0550-3213
1873-1562
Publication date 1997-10
Sub-type Article (original research)
Open Access Status File (Publisher version)
Volume 502
Issue 3
Start page 649
End page 670
Total pages 22
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Language eng
Abstract In this paper we consider Wakimoto free field realizations of simple affine Lie algebras, a subject already much studied. We present three new sets of results, (i) Based on quantizing differential operator realizations of the corresponding Lie algebras we provide general universal very simple expressions for all currents, more compact than has been established so far. (ii) We supplement the treatment of screening currents of the first kind, known in the literature, by providing a direct proof of the properties for screening currents of the second kind. Finally (iii) we work out explicit free field realizations of primary fields with general non-integer weights. We use a formalism where the (generally infinite) multiplet is replaced by a generating function primary operator. These results taken together allow setting up integral representations for correlators of primary fields corresponding to non-integrable degenerate (in particular admissible) representations.
Keyword CONFORMAL FIELD THEORY
AFFINE CURRENT ALGEBRA
FREE FIELD REALIZATIONS
SL(2) CURRENT-ALGEBRA
KNIZHNIK-ZAMOLODCHIKOV EQUATION
FEIGIN-FUCHS REPRESENTATIONS
DIMENSIONAL LIE-ALGEBRAS
QUANTUM GROUP-STRUCTURE
ZUMINO-WITTEN MODEL
KAC-MOODY ALGEBRAS
OPERATOR ALGEBRA
BRST COHOMOLOGY
WZNW MODELS
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, 11 Apr 2012, 16:23:04 EST by Kay Mackie on behalf of Mathematics