Ultraviolet Property of Noncommutative Wess-Zumino-Witten Model

TL;DR

This paper constructs a noncommutative version of the Wess-Zumino-Witten model and investigates its ultraviolet properties, revealing similarities to the commutative case and identifying a fixed point in the U(1) model.

Contribution

It introduces a noncommutative extension of the WZW model and analyzes its ultraviolet behavior, highlighting new fixed point structures.

Findings

The eta-function resembles that of the ordinary WZW model.

The U(1) noncommutative model exhibits a nontrivial fixed point.

The ultraviolet properties are consistent with known models.

Abstract

We construct noncommutative extension of the Wess-Zumino-Witten (WZW) model and study its ultraviolet property. The \beta-function of the U(N) noncommutative WZW model resembles that of the ordinary WZW model. The U(1) noncommutative model has also a nontrivial fixed point.