We consider the type-IIB background generated by the strong-coupling limit of Nc D5 branes wrapped on S2, and focus our attention on a special class of solutions that exhibit walking behavior. We compute numerically the spectrum of scalar fluctuations around vacua of this class. Besides two cuts, and sequences of single poles converging on one of the branch points, the spectrum contains one isolated scalar, the mass of which is suppressed by the length of the walking region. Approximate scale-invariance symmetry in the walking region suggests that this be interpreted as a light dilaton, the pseudo-Goldstone boson of dilatations.Comment: 4 pages, 3 figures. Superpotential formalism replaced with effective potential. Main results unchange

We consider renormalization group flows between conformal field theories in five (six) dimensions with a string (M-theory) dual. By compactifying on a circle (torus) with appropriate boundary conditions, we obtain continuous families of confining fourdimensional theories parametrized by the ratio Λ flow /Λ QCD , with Λ flow the scale at which the flow between fixed points takes place and Λ QCD the confinement scale. We construct the dual geometries explicitly and compute the spectrum of scalar bound states (glueballs). We find a 'universal' subset of states common to all the models. We comment on the modifications of these models, and the corresponding fine-tuning, required for a parametrically light 'dilaton' state to be present. We also comment on some aspects of these theories as probed by extended objects such as strings and branes.

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.Comment: 39 pages. 11 figures. Published versio

We reconsider a one-parameter class of known solutions of the circle compactification of Romans six-dimensional half-maximal supergravity. The gauge-theory duals of these solutions are confining four-dimensional field theories. Their UV completions consist of the compactification on a circle of a higher-dimensional field theory that is flowing between two fixed points in five dimensions. We systematically study the bosonic fluctuations of the supergravity theory, corresponding to the bosonic glueballs of the dual field theory.We perform numerically the calculation of the spectrum of excitations of all the bosonic fields, several of which had been disregarded in earlier work on the subject. We discuss the results as a function of the one parameter characterising the class of background solutions, hence further extending known results. We show how certain towers of states are independent of the background, and compare these states to existing lattice literature on four-dimensional Yang-Mills (pure) gauge theories, confirming the existence of close similarities.For the aforementioned analysis, we construct gauge-invariant combinations of the fields appearing in the reduction to five dimensions of the supergravity theory, and hence focus on the 32 physical bosonic degrees of freedom. We show explicitly how to implement gaugefixing of the supergravity theory. The results of such technical work could be used to analyse the spectra of other theories proposed in the context of top-down holography. For example, it could be applied to holographic realisations of composite-Higgs and light-dilaton scenarios.