  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 gauge-fixing 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.
