  We discuss the statistical properties of a single vortex line in a perfect
fluid. The partition function is calculated up to the end in the thin vortex
approximation. It turns out that corresponding theory is renormalizable, and
the renormalization law for the core size of the vortex is found. The direction
of renormalization group flow makes the thin vortex approximation to be valid
for the interest cases and this result does not depend on the choice of
infrared regularization. The expressions for some gauge-invariant correlators
are obtained to demonstrate the developed formalism at work.
