  Four dimensional Yang-Mills theory formulated through an action on twistor
space has a larger gauge symmetry than the usual formulation, which in previous
work was shown to allow a simple gauge transformation between text-book
perturbation theory and the Cachazo-Svrcek-Witten rules. In this paper we study
non-supersymmetric twistor Yang-Mills theory at loop level using the background
field method. For an appropriate partial quantum field gauge choice it is shown
the calculation of the effective action is equivalent to (the twistor lift of)
the calculation in ordinary Yang-Mills theory in the Chalmers and Siegel
formulation to all orders in perturbation theory. A direct consequence is that
the twistor version of Yang-Mills theory is just as renormalizable in this
particular gauge. As applications an explicit calculation of the Yang-Mills
beta function and some preliminary investigations into using the formalism to
calculate S-matrix elements at loop level are presented. In principle the
technique described in this paper generates consistent quantum completions of
the CSW rules. However, by inherent limitations of the partial gauge choice
employed here, this offers in its current form mainly simplifications for tree
level forestry. The method is expected to be applicable to a wide class of four
dimensional gauge theories.
