A study of holographic renormalization group flows in d=6 and d=3

We present an explicit study of the holographic renormalization group (RG) in six dimensions using minimal gauged supergravity. By perturbing the theo ry with the addition of a relevant operator of dimension four one flows to a non-supersymmetric conformal fixed point. There are also solutions descri bing non-conformal vacua of the same theory obtained by giving an expectati on value to the operator. One such vacuum is supersymmetric and is obtained by using the true superpotential of the theory. We discuss the physical ac ceptability of these vacua by applying the criteria recently given by Gubse r for the four-dimensional case and find that those criteria give a clear p hysical picture in the six-dimensional case as well. We use this example to comment on the role of the Hamilton-Jacobi equations in implementing the R G. We conclude with some remarks on AdS(4) and the status of three-dimensio nal superconformal theories from squashed solutions of M-theory.