A Variational Principle for Radial Flows in Holographic theories
R. Akhoury
Abstract
We develop furthur the correspondence between a d+1 dimensional theory and a d dimensional one with the "radial" (d+1)th corodinate ρplaying the role of an evolution parameter. We discuss the evolution of an effective action defined on a d dimensional surface charactarized by ρby means of a new variational principle. The conditions under which the flow equations are valid are discussed in detail as is the choice of boundary conditions. It is explained how domain walls may be incorporated in the framework and some generalized junction conditions are obtained. The general principles are illustrated on the example of a supergravity theory on AdSd+1.
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