Maximally supersymmetric RG flows and AdS duality

We discuss four-dimensional renormalization group flows which preserve sixteen supersymmetries. In the infrared, these can be viewed as deformations of the N = 4 superconformal fixed points by special, irrelevant operators. It is argued that the gauge coupling beta function continues to vanish identically, for all coupling constants and energy scales, for such RG hows. In addition, the dimensions of all operators in short supersymmetry representations are constant along such flows. This is compatible with a conjectured generalization of the AdS/CFT correspondence which describes such flows, e.g., the D3-brane vacuum before taking the near-horizon limit. RG flows in three and six dimensions, preserving 16 supersymmetries, are also briefly discussed, including a discussion of generalized AdS/CFT duality for the M2- and M5-brane cases. Finally, we discuss maximally supersymmetric RG hows associated with noncommutative geometry. (C) 2000 Elsevier Science B.V. All rights reserved.