{
  "id": "hep-th/9605102",
  "version": "v3",
  "published": "1996-05-15T05:30:26.000Z",
  "updated": "1996-05-20T01:17:08.000Z",
  "title": "An explicit construction of Wakimoto realizations of current algebras",
  "authors": [
    "Jan de Boer",
    "Laszlo Feher"
  ],
  "comment": "13 pages, LaTeX; a typo corrected in (5.5-6), refs and a remark added",
  "journal": "Mod.Phys.Lett. A11 (1996) 1999-2012",
  "doi": "10.1142/S0217732396001995",
  "categories": [
    "hep-th",
    "math.QA",
    "q-alg"
  ],
  "abstract": "It is known from a work of Feigin and Frenkel that a Wakimoto type, generalized free field realization of the current algebra $\\widehat{\\cal G}_k$ can be associated with each parabolic subalgebra ${\\cal P}=({\\cal G}_0+{\\cal G}_+)$ of the Lie algebra ${\\cal G}$, where in the standard case ${\\cal G}_0$ is the Cartan and ${\\cal P}$ 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 ${\\cal G}$-valued current in terms of symplectic bosons belonging to ${\\cal G}_+$ and a current belonging to ${\\cal G}_0$. 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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1996-05-20T01:17:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "current algebra",
      "wakimoto realization",
      "explicit construction",
      "generalized free field realization",
      "poisson bracket realization"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 418585
    }
  }
}