Renormalization-group flows from five-dimensional supergravity

The way in which supergravity correctly describes an N = 1 supersymmetric renormalization-group (RG) flow, and how this flow can be checked against known field theory results are discussed. A by-product of this study of renormalization-group flows is the discovery of a general c-theorem for any such flow described via supergravity. In the second part of the paper some older issues in supergravity are examined, most particularly that of consistent truncation, and the relevance of these issues to the phase structure and flows in Yang-Mills theory is discussed. The final part of the paper focuses on how supergravity distinguishes between perturbations of the Yang-Mills action and states in the Hilbert space. As an illustration of this the supergravity description of part of the Coulomb branch of the N = 4 supersymmetric Yang-Mills theory is explored.