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.
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