Wakimoto realizations of current algebras

An explicit construction

Jan De Boer, L. Fehér

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

A generalized Wakimoto realization of ĜK can be associated with each parabolic subalgebra P = (G0 + G+) of a simple Lie algebra G according to an earlier proposal by Feigin and Frenkel. In this paper the proposal is made explicit by developing the construction of Wakimoto realizations from a simple but unconventional viewpoint. An explicit formula is derived for the Wakimoto current first at the Poisson bracket level by Hamiltonian symmetry reduction of the WZNW model. The quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate ĜK by means of commutators. The affine-Sugawara stress-energy tensor is verified to have the expected quadratic form in the constituents, which are symplectic bosons belonging to G+ and a current belonging to G0. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold P\G. The effect of this choice is investigated in detail by constructing quantum coordinate transformations. Finally, the explicit form of the screening charges for each generalized Wakimoto realization is determined, and some applications are briefly discussed.

Original languageEnglish
Pages (from-to)759-793
Number of pages35
JournalCommunications in Mathematical Physics
Volume189
Issue number3
Publication statusPublished - 1997

Fingerprint

Current Algebra
current algebra
proposals
Quantization
Symmetry Reduction
Flag Manifold
Poisson Bracket
Simple Lie Algebra
commutators
coordinate transformations
Coordinate Transformation
brackets
Commutator
Quadratic form
Bosons
Subalgebra
Screening
Explicit Formula
polynomials
algebra

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Wakimoto realizations of current algebras : An explicit construction. / De Boer, Jan; Fehér, L.

In: Communications in Mathematical Physics, Vol. 189, No. 3, 1997, p. 759-793.

Research output: Contribution to journalArticle

@article{97e14a33aebd4c7e8a5fc9e4e20e27e0,
title = "Wakimoto realizations of current algebras: An explicit construction",
abstract = "A generalized Wakimoto realization of ĜK can be associated with each parabolic subalgebra P = (G0 + G+) of a simple Lie algebra G according to an earlier proposal by Feigin and Frenkel. In this paper the proposal is made explicit by developing the construction of Wakimoto realizations from a simple but unconventional viewpoint. An explicit formula is derived for the Wakimoto current first at the Poisson bracket level by Hamiltonian symmetry reduction of the WZNW model. The quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate ĜK by means of commutators. The affine-Sugawara stress-energy tensor is verified to have the expected quadratic form in the constituents, which are symplectic bosons belonging to G+ and a current belonging to G0. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold P\G. The effect of this choice is investigated in detail by constructing quantum coordinate transformations. Finally, the explicit form of the screening charges for each generalized Wakimoto realization is determined, and some applications are briefly discussed.",
author = "{De Boer}, Jan and L. Feh{\'e}r",
year = "1997",
language = "English",
volume = "189",
pages = "759--793",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Wakimoto realizations of current algebras

T2 - An explicit construction

AU - De Boer, Jan

AU - Fehér, L.

PY - 1997

Y1 - 1997

N2 - A generalized Wakimoto realization of ĜK can be associated with each parabolic subalgebra P = (G0 + G+) of a simple Lie algebra G according to an earlier proposal by Feigin and Frenkel. In this paper the proposal is made explicit by developing the construction of Wakimoto realizations from a simple but unconventional viewpoint. An explicit formula is derived for the Wakimoto current first at the Poisson bracket level by Hamiltonian symmetry reduction of the WZNW model. The quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate ĜK by means of commutators. The affine-Sugawara stress-energy tensor is verified to have the expected quadratic form in the constituents, which are symplectic bosons belonging to G+ and a current belonging to G0. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold P\G. The effect of this choice is investigated in detail by constructing quantum coordinate transformations. Finally, the explicit form of the screening charges for each generalized Wakimoto realization is determined, and some applications are briefly discussed.

AB - A generalized Wakimoto realization of ĜK can be associated with each parabolic subalgebra P = (G0 + G+) of a simple Lie algebra G according to an earlier proposal by Feigin and Frenkel. In this paper the proposal is made explicit by developing the construction of Wakimoto realizations from a simple but unconventional viewpoint. An explicit formula is derived for the Wakimoto current first at the Poisson bracket level by Hamiltonian symmetry reduction of the WZNW model. The quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate ĜK by means of commutators. The affine-Sugawara stress-energy tensor is verified to have the expected quadratic form in the constituents, which are symplectic bosons belonging to G+ and a current belonging to G0. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold P\G. The effect of this choice is investigated in detail by constructing quantum coordinate transformations. Finally, the explicit form of the screening charges for each generalized Wakimoto realization is determined, and some applications are briefly discussed.

UR - http://www.scopus.com/inward/record.url?scp=0031549889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031549889&partnerID=8YFLogxK

M3 - Article

VL - 189

SP - 759

EP - 793

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -