An explicit construction of Wakimoto realizations of current algebras

Jan De Boer, László Fehér

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

It is known from a work of Feigin and Frenkel that a Wakimoto type, generalized free field realization of the current algebra Ĝk can be associated with each parabolic subalgebra P = (G0 + G+) of the Lie algebra G, where in the standard case G0 is the Cartan and P is the Borel subalgebra. In this letter we obtain an explicit formula for the Wakimoto realization in the general case. Using Hamiltonian reduction of the WZNW model, we first derive a Poisson bracket realization of the G-valued current in terms of symplectic bosons belonging to G+ and a current belonging to G0. We then quantize the formula by determining the correct normal ordering. We also show that the affine-Sugawara stress-energy tensor takes the expected quadratic form in the constituents.

Original languageEnglish
Pages (from-to)1999-2011
Number of pages13
JournalModern Physics Letters A
Volume11
Issue number24
DOIs
Publication statusPublished - Jan 1 1996

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Astronomy and Astrophysics
  • Physics and Astronomy(all)

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