Partial restoration of chiral symmetry in a confining string

TL;DR

This paper models the relationship between confinement and chiral symmetry breaking in QCD using a string model, predicting the chiral condensate distribution and validating it against lattice QCD results.

Contribution

It introduces an effective 1+1D string worldsheet model to analytically describe chiral condensate behavior in the confining string, linking it to the chiral anomaly and vacuum structure.

Findings

Analytical prediction of chiral condensate distribution in the transverse plane.

Good agreement between the model's predictions and lattice QCD results.

Demonstration of the string model's effectiveness in describing chiral symmetry aspects.

Abstract

We attempt to describe the interplay of confinement and chiral symmetry breaking in QCD by using the string model. We argue that in the quasi-abelian picture of confinement based on the condensation of magnetic monopoles and the dual Meissner effect, the worldsheet dynamics of the confining string can be effectively described by the $1+1$ dimensional massless electrodynamics, which is exactly soluble. The transverse plane distribution of the chromoelectric field stretched between the quark and antiquark sources can then be attributed to the fluctuations in the position of the string. The dependence of the chiral condensate in the string on the (chromo-)electric field can be evaluated analytically, and is determined by the chiral anomaly and the $\theta$-vacuum structure. Therefore, our picture allows to predict the distribution of the chiral condensate in the plane transverse to the axis connecting the quark and antiquark. This prediction is compared to the lattice QCD results; a good agreement is found.