The Exact Tachyon Beta-Function for the Wess-Zumino-Witten Model

TL;DR

This paper derives an exact expression for the tachyon beta-function in the Wess-Zumino-Witten model and verifies it through three-loop calculations in a general non-linear sigma model with torsion.

Contribution

It provides the first exact formula for the tachyon beta-function in the WZW model, validated by higher-loop calculations in related models.

Findings

Exact tachyon beta-function derived for WZW model

Validation through three-loop calculations in non-linear sigma models

Confirmation of the formula's accuracy up to three loops

Abstract

We derive an exact expression for the tachyon $\beta$-function for the Wess-Zumino-Witten model. We check our result up to three loops by calculating the three-loop tachyon $\beta$-function for a general non-linear $\sigma$-model with torsion, and then specialising to the case of the WZW model.