  The existence of a {\it stable critical point}, separate from the Gaussian
and XY critical points, of the Ginzburg-Landau theory for superconductors, is
demonstrated by direct extraction via Monte-Carlo simulations, of a negative
anomalous dimension $\eta_{\phi}$ of a complex scalar field $\phi$ forming a
dual description of a neutral superfluid. The dual of the neutral superfluid is
isomorphic to a charged superfluid coupled to a massless gauge-field. The
anomalous scaling dimension of the superfluid order-field is positive, while we
find that the anomalous dimension of the dual field is negative. The dual
gauge-field does not decouple from the dual complex matter-field at the
critical point. {\it These two critical theories represent separate fixed
points.} The physical meaning of a negative $\eta_{\phi}$ is that the
vortex-loop tangle of the superfluid at the critical point fills space {\it
more} efficiently than random walkers, {\it without collapsing}. This is due to
the presence of the massless dual gauge-field, and the resulting long-ranged
{\it vectorial} Biot-Savart interaction between vortex-loop segments, which is
a relevant perturbation to the steric $|\psi|^4$ repulsion term. Hence, the
critical dual theory is not in the universality class of the $|\psi|^4$-theory.
