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

Abstract

We point out that the permanent confinement in a compact (2+1)-dimensional U(1) 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+1)-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( l) of the theory show that the renormalization of K( l) induces an anomalous scaling dimension η y of y( l). The stiffness parameter of the theory has a universal jump at the transition determined by the dimensionality and η 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 ν 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.