Vortices on the worldsheet of the QCD string

TL;DR

This paper studies the behavior of the QCD string in various dimensions with periodic transverse directions, proposing an effective string theory that predicts a vortex-driven Kosterlitz-Thouless transition affecting the string's properties.

Contribution

It introduces an effective string action incorporating transverse size dependence and predicts a universal vortex-driven phase transition in the worldsheet theory.

Findings

Predicts a Kosterlitz-Thouless transition at a specific string tension and transverse size.

Shows the effective central charge decreases by one unit after the transition.

Accounts for the evolution of the Luscher term with transverse dimension size.

Abstract

We investigate the properties of the QCD string in the Euclidean SU(N) pure gauge theory when the space-time dimensions transverse to it are periodic. From the point of view of an effective string theory, the string tension $\sigma$ and the low-energy constants $c_k$ of the theory are arbitrary functions of the sizes of the transverse dimensions L_p. Since the gauge theory is linearly confining in D=2, 3 and 4 dimensions, we propose an effective string action for the flux-tube energy levels at any choice of $L_p$, given $\sigma(L_p)$ and $c_k(L_p)$. The Luscher term only depends on the number of massless bosonic degrees of freedom and the effective theory can account for its evolution as a function of $L_p$. As the size of one transverse dimension is varied, we predict a Kosterlitz-Thouless transition of the worldsheet field theory at $\sigma(L_p)L_p^2 \simeq 1/8\pi $ driven by vortices, after which the periodic component of the worldsheet displacement vector develops a mass gap and the effective central charge drops by one unit. The universal properties of the transition are emphasised.