  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
$\eta_y$ 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 {\it 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 $\nu$ 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.
