An explicit construction of Wakimoto realizations of current algebras

Details An explicit construction of Wakimoto realizations of current algebras An explicit construction of Wakimoto realizations of current algebras

1996-05-15

arxiv.org/abs/hep-th/9605102v3

Mod.Phys.Lett. A11 (1996) 1999-2012

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LaTeX; a typo corrected in (5.5-6), refs and a remark added

Scientific paper

10.1142/S0217732396001995

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.

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