Secrets of the metric in N=4 and N=2*geometries

The metric of the gravity dual of a field theory should contain precisely t he same information as the field theory. We discuss this connection in the N = 4 theory where a scalar vev may be introduced at the level of 5d superg ravity and the solutions lifted to 10d. We stress the role of brane probing in finding the coordinates appropriate to the field theory. In these coord inates the metric parametrizes the gauge invariant operators of the field t heory and either side of the duality is uniquely determined by the other. W e follow this same chain of computations for the 10d lift of the N = 2* geo metry of Pilch and Warner. The brane probe of the metric reveals the 2d mod uli space and the functional form of the gauge coupling. In the coordinates appropriate to the field theory the metric on moduli space takes a very si mple form and one can read off the gravity predictions for operators in the field theory. Surprisingly there is logarithmic renormalization even in th e far UV where the field theory reverts to N = 4 super Yang-Mills. We exten d the analysis of Buchel et al to find the D3-brane source distribution tha t generates the supergravity prediction for the gauge coupling for the whol e class of solutions corresponding to different points on moduli space. Thi s distribution does not account for the logarithmic behaviour in the rest o f the metric though. We discuss possible resolutions of the discrepancy.