Wakimoto realizations of current algebras: an explicit construction

PDF Version Also Available for Download.

Description

A generalized Wakimoto realization of $\widehat\cal G_K$ can be associated with each parabolic subalgebra $\cal P=(\cal G_0 +\cal G_+)$ of a simple Lie algebra $\cal G$ 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 ... continued below

Creation Information

de Boer, Jan & Feher, Laszlo November 12, 1996.

Context

This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

Who

People and organizations associated with either the creation of this article or its content.

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

Description

A generalized Wakimoto realization of $\widehat\cal G_K$ can be associated with each parabolic subalgebra $\cal P=(\cal G_0 +\cal G_+)$ of a simple Lie algebra $\cal G$ 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 $\widehat\cal G_K$ 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 $\cal G_+$ and a current belonging to $\cal G_0$. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold $P\backslash G$. 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.

Source

  • Journal Name: Communications in Mathematical Physics; Related Information: Journal Publication Date: 11/01/1997

Language

Item Type

Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

  • Report No.: LBNL-39562
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 965357
  • Archival Resource Key: ark:/67531/metadc930038

Collections

This article is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

What responsibilities do I have when using this article?

When

Dates and time periods associated with this article.

Creation Date

  • November 12, 1996

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

Description Last Updated

  • Nov. 18, 2016, 3:36 p.m.

Usage Statistics

When was this article last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 3

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

de Boer, Jan & Feher, Laszlo. Wakimoto realizations of current algebras: an explicit construction, article, November 12, 1996; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc930038/: accessed July 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.