The WZNW Model at Two Loops

TL;DR

This paper performs a perturbative analysis of the conformal WZNW model at one and two loops, revealing that the two-point function vanishes at two loops and confirming the level shift in the effective action.

Contribution

It provides a detailed two-loop calculation of current correlation functions in the WZNW model, confirming the level shift and demonstrating the insensitivity to regularization details.

Findings

Two-loop two-point function vanishes (up to infrared logs)

Effective action matches original with level shift k→k+ĥ

Results are insensitive to tensor treatment in dimensional regularization

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 $R^*$ 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, $k\to k+\tilde h$.