  We study the renormalization of a general field theory on the 2-sphere with
tensorial interaction and gauge invariance under the diagonal action of SU(2).
We derive the power counting for arbitrary dimension d. For the case d=4, we
prove perturbative renormalizability to all orders via multi-scale analysis,
study both the renormalised and effective perturbation series, and establish
the asymptotic freedom of the model. We also outline a general power counting
for the homogeneous space SO(D)/SO(D-1), of direct interest for quantum gravity
models in general dimensions, and point out the obstructions to the direct
generalisation of our results to these cases.
