Wakimoto realizations of current algebras: An explicit construction

Jan De Boer, László Fehér

Research output: Article

22 Citations (Scopus)


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
Issue number3
Publication statusPublished - 1997

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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