  I study the normal-to-superconducting (NS) transition within the
Ginzburg-Landau (GL) model, taking into account the fluctuations in the
$m$-component complex order parameter $\psi\a$ and the vector potential $\vec
A$ in the arbitrary dimension $d$, for any $m$. I find that the transition is
of second-order and that the previous conclusion of the fluctuation-driven
first-order transition is an artifact of the breakdown of the $\eps$-expansion
and the inaccuracy of the $1/m$-expansion for physical values $\eps=1$, $m=1$.
I compute the anomalous $\eta(d,m)$ exponent at the NS transition, and find
$\eta (3,1)\approx-0.38$. In the $m\to\infty$ limit, $\eta(d,m)$ becomes exact
and agrees with the $1/m$-expansion. Near $d=4$ the theory is also in good
agreement with the perturbative $\eps$-expansion results for $m>183$ and
provides a sensible interpolation formula for arbitrary $d$ and $m$.
