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Multiscale confining dynamics from holographic RG flows

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 four-dimensional theories parametrized by the ratio $Λ_{\rm {\tiny flow}}/Λ_{\rm \tiny{QCD}}$, with $Λ_{\rm \tiny{flow}}$ the scale at which the flow between fixed points takes place and $Λ_{\rm \tiny{QCD}}$ 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.