Towards a Theory of the QCD String

TL;DR

This paper introduces a new integrable four-dimensional relativistic string model featuring a worldsheet axion, connecting theoretical predictions with lattice data on confining flux tubes in gluodynamics.

Contribution

It constructs a novel integrable string model with a worldsheet axion and links it to lattice observations of pseudoscalar particles in gluodynamics.

Findings

The model's coupling fixed at Q≈0.37 by integrability.

Lattice data shows a pseudoscalar axion with coupling Q_L≈0.38±0.04.

The model extends non-critical string theories with new integrable features.

Abstract

We construct a new model of four-dimensional relativistic strings with integrable dynamics on the worldsheet. In addition to translational modes this model contains a single massless pseudoscalar worldsheet field - the worldsheet axion. The axion couples to a topological density which counts the self-intersection number of a string. The corresponding coupling is fixed by integrability to $Q=\sqrt{7\over 16\pi}\approx 0.37$. We argue that this model is a member of a larger family of relativistic non-critical integrable string models. This family includes and extends conventional non-critical strings described by the linear dilaton CFT. Intriguingly, recent lattice data in $SU(3)$ and $SU(5)$ gluodynamics reveals the presence of a massive pseudoscalar axion on the worldsheet of confining flux tubes. The value of the corresponding coupling, as determined from the lattice data, is equal to $Q_L\approx0.38\pm0.04$.