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Screening currents Ward identity and integral formulas for the WZNW correlation functions. (English) Zbl 0832.17030

Kato, Mitsuhiro (ed.) et al., Recent developments in string and field theory. Kyoto: Yukawa Institute for Theoretical Physics and The Physical Society of Japan, Prog. Theor. Phys., Suppl. 110, 303-319 (1992).
From the introduction: In the Wess-Zumino-Novikov-Witten (WZNW) models, the correlation function can be characterized as the solution of the Knizhnik-Zamolodchikov (KZ) equation. The integral representation for this correlation function can be obtained from the free field realization of the Kac-Moody algebras (the Wakimoto realization). This realization has been discussed by several authors, and its general properties have been clarified. In this method, the correlation function is represented by some integral of the free fields correlation. But, for arbitrary algebras and representations, it is difficult to evaluate the free fields correlation except in some particular cases. This is entirely due to the complicated structure of the realization. In a previous paper, the author, A. Tsuchiya and Y. Yamada [Nucl. Phys. B 365, 680 (1991)]solved this problem and derived the integral representation for the WZNW models corresponding to arbitrary simple Lie algebras. By using the “screening currents Ward identity”, we obtained an exact result without treating the complicated explicit form of the Wakimoto realization.
This paper is a more complete version of the paper cited above, and contains some explicit examples in the case of \(\widehat {\mathfrak {sl} (3)}\) and refined proofs.
For the entire collection see [Zbl 0822.00016].

MSC:

17B81 Applications of Lie (super)algebras to physics, etc.
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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