Kosterlitz-Thouless-like deconfinement mechanism in the (2+1)-dimensional Abelian Higgs model

We point out that the permanent confinement in a compact (2 + I)-dimensional U(I) Abelian Higgs model is destroyed by matter fields in the fundamental representation. The deconfinement transition is Kosterlitz-Thouless-like. The dual theory is shown to describe a three-dimensional gas of point charges with logarithmic interactions which arises from an anomalous dimension of the gauge field caused by critical matter field fluctuations. The theory is equivalent to a sine-Gordon-like theory in (2 + I)-dimensions with an anomalous gradient energy proportional to k(3). The Callan-Symanzik equation is used to demonstrate that this theory has a massless and a massive phase. The renormalization group equations for the fugacity y(l) and stiffness parameter K (1) of the theory show that the renormalization of K(1) induces an anomalous scaling dimension eta(y) of y(l). The stiffness parameter of the theory has a universal jump at the transition determined by the dimensionality and eta(y). As a byproduct of our analysis, we relate the critical coupling of the sine-Gordon-like theory to an a priori arbitrary constant that enters into the computation of critical exponents in the Abelian Higgs model at the charged infrared-stable fixed point of the theory, enabling a determination of this parameter. This facilitates the computation of the critical exponent v at the charged fixed point in excellent agreement with one-loop renormalization group calculations for the three-dimensional XY model, thus confirming expectations based on duality transformations. (C) 2003 Elsevier B.V. All rights reserved.