Vortices on the worldsheet of the QCD string

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 σ and the low-energy constants c k of the theory are arbitrary functions of the sizes of the transverse dimensions L ⊥ . 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 ⊥ , given σ ( L ⊥ ) and c k ( L ⊥ ) . The Lüscher 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 ⊥ . As the size of one transverse dimension is varied, we predict a Kosterlitz–Thouless transition of the worldsheet field theory at σ ( L ⊥ ) L ⊥ 2 ≃ 1 / 8 π 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.