Hamiltonian reduction of SL(2) theories at the level of correlators

Petersen, J. L., Rasmussen, J. and Yu, M. (1995) Hamiltonian reduction of SL(2) theories at the level of correlators. Nuclear Physics B, 457 1-2: 343-356. doi:10.1016/0550-3213(95)00503-X


Author Petersen, J. L.
Rasmussen, J.
Yu, M.
Title Hamiltonian reduction of SL(2) theories at the level of correlators
Journal name Nuclear Physics B   Check publisher's open access policy
ISSN 0550-3213
1873-1562
Publication date 1995-12-01
Sub-type Article (original research)
DOI 10.1016/0550-3213(95)00503-X
Open Access Status DOI
Volume 457
Issue 1-2
Start page 343
End page 356
Total pages 14
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Language eng
Formatted abstract
Since the work of Bershadsky and Ooguri and Feigin and Frenkel it is well known that correlators of SL(2) current algebra for admissible representations should reduce to correlators for conformal minimal models. A precise proposal for this relation has been given at the level of correlators: When SL(2) primary fields are expressed as γj(zn, xn) with xn being a variable to keep track of the SL(2) representation multiplet (possibly infinitely dimensional for admissible representations), then the minimal model correlator is supposed to be obtained simply by putting all xn = Zn. Although strong support for this has been presented, to the best of our understanding a direct, simple proof seems to be missing so in this paper we present one based on the free field Wakimoto construction and our previous study of that in the present context. We further verify that the explicit SL(2) correlators we have published in a recent preprint reduce in the above way, up to a constant which we also calculate. We further discuss the relation to more standard formulations of hamiltonian reduction.
Keyword KNIZHNIK-ZAMOLODCHIKOV EQUATION
FOCK REPRESENTATIONS
CURRENT-ALGEBRA
MINIMAL 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: Thu, 12 Apr 2012, 02:33:09 EST by Kay Mackie on behalf of Mathematics