group is trivial. Examples of quantum field theories that are not conformal have a much richer renormalization group evolution and may provide valuable insights into the role of the “fifth dimension”. In this case, we are able to determine the first corrections to the AdS$_{5}$ geometry. This approximate background leads to corrections to the four derivative terms in the probe action that are consistent with the form of instanton corrections to the four derivative terms in the field theory. Our results strongly suggest that the probe worldvolume action reproduces the exact Wilsonian effective action of the field theory. We also compute the quark-antiquark potential in this geometry.

Our third and final example considers the pure gauge theory. We are able to find an approximate solution, valid when the separation between the probe and source is large. This geometry reproduces the correct [*semiclassical*]{} structure of the four derivative terms. It would thus seem that the background we have found is capable of describing [*perturbative*]{} field theory on the probe world volume. By explicitly computing the magnitude of the square of the Ricci tensor, we are able to explain why this is indeed the case.

When this work was near completion we 