The WZNW Model at Two Loops

Abstract

We study perturbatively the (conformal) WZNW model. At one loop we compute one-particle irreducible two- and three-point current correlation functions, both in the conventional version and in the classically equivalent, chiral, nonlocal, induced version of the model. At two loops we compute the two-point function and find that it vanishes (modulo infrared-induced logarithms). We use dimensional regularization and the $R^{\ast }$ operation for removing infrared divergences. The outcome of the calculations is insensitive to the treatment of the $\varepsilon^{\m\n}$ tensor as a two-dimensional or $d$-dimensional object. Our results indicate that the one-particle irreducible current correlation functions constitute an effective action equal to the original WZNW action with the familiar level shift, $k\to k+\tilde{h}$.

40 pages, Latex, (4 postscript figures at end of file, to be split off into files called diag1.ps,...,diag4.ps),THU-93/15

References in corpus (2)

• Effective action of gauged WZW model and exact string solutions
• Induced (N,0) supergravity as a constrained Osp(N,2) WZWN model and its effective action

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