  We construct an effective low energy Lagrangian of gluodynamics which (i)
satisfies all constraints imposed by the Renormalization Group; (ii) is scale
and conformally invariant in the limit of vanishing vacuum energy density;
(iii) matches onto the perturbative theory at short distances. This effective
theory has a dual description as classical gluodynamics on a curved conformal
background. Color fields are dynamically confined, and the strong coupling
freezes at distances larger than the glueball size. We also make specific
predictions (in particular, on the Nc dependence of glueball properties) which
can be tested in lattice simulations of gluodynamics.
