We construct an effective low energy Lagrangian using constraints imposed by the renormalization group. Degrees of freedom are gluons and a scalar glueball. 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 make specific predictions (in particular, on the Nc dependence of glueball properties) which can be tested in lattice simulations of gluodynamics.