# From QCD Strings to WZW

## TL;DR

This paper explores the theoretical properties of axionic strings in pure gluodynamics, showing that their worldsheet dynamics in the infinite tension limit are described by an $O(D-2)$ Wess--Zumino--Witten model, revealing a new integrable string class.

## Contribution

It introduces a novel connection between axionic strings and the $O(D-2)$ WZW model, expanding understanding of non-critical integrable string theories.

## Key findings

- Worldsheet axions are described by a 'pseudofree' theory with trivial S-matrix.
- In the infinite tension limit, axionic strings correspond to the $O(D-2)$ WZW model.
- The action cannot be simplified to a free theory by local field redefinitions.

## Abstract

According to the Axionic String Anstaz (ASA) confining flux tubes in pure gluodynamics are in the same equivalence class as a new family of integrable non-critical strings, called axionic strings. In addition to translational modes, axionic strings carry a set of worldsheet axions transforming as an antisymmetric tensor under the group of transverse rotations. We initiate a study of integrable axionic strings at general number of space-time dimensions $D$. We show that in the infinite tension limit worldsheet axions should be described by a peculiar "pseudofree" theory---their $S$-matrix is trivial, but the corresponding action cannot be brought into a free form by a local field redefinition. This requirement fixes the axionic action to take a form of the $O(D-2)$ Wess--Zumino--Witten (WZW) model.