Vortices on the worldsheet of the QCD string

Details Vortices on the worldsheet of the QCD string Vortices on the worldsheet of the QCD string

2005-06-03

arxiv.org/abs/hep-th/0506034v1

Nucl.Phys. B724 (2005) 432-450

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 1figure

Scientific paper

10.1016/j.nuclphysb.2005.07.001

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.

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