  We consider a general five-dimensional sigma-model coupled to gravity, with
any number of scalars and general sigma-model metric and potential. We discuss
in detail the problem of the boundary conditions for the scalar fluctuations,
in the case where the fifth dimension is compact, and provide a simple (and
very general) algorithmic procedure for computing the spectrum of physical
scalar fluctuations of the fully back-reacted system. Focusing in particular on
the conditions under which the spectrum of scalar excitations (glueballs)
contains parametrically light states, we apply the formalism to some especially
simple toy models, which can be thought of as the gauge/gravity duals of
strongly-coupled, non-conformal four-dimensional gauge theories. Our examples
are chosen both within the context of phenomenological effective field theory
constructions (bottom-up approach), and within the context of consistent
truncations of ten-dimensional string theories in the supergravity limit
(top-down approach). In one of the examples, a light dilaton is present in the
spectrum in spite of the presence of a bad naked singularity in the deep IR,
near which the RG flow of the dual theory is certainly very far away from any
fixed point. If this feature were to persist in a complete model in which the
singularity is resolved, this would prove that a light dilaton is to be
expected in at least certain walking technicolor theories. We provide here all
the technical details for testing this statement, once such a complete model is
identified.
