QCD in curved space-time: a conformal bag model

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.