  We discuss the phase structure of N D4 branes wrapped on a temporal
(Euclidean) and a spatial circle, in terms of the near-horizon AdS geometries.
This system has been studied previously to understand four dimensional pure
SU(N) Yang-Mills theory (YM4) through holography. In the usual treatment of the
subject, the phase transition between the AdS soliton and the black D4 brane is
interpreted as the strong coupling continuation of the
confinement/deconfinement transition in YM4. We show that this interpretation
is not valid, since the black D4 brane and the deconfinement phase of YM4 have
different realizations of the Z_N centre symmetry and cannot be identified. We
propose an alternative gravity dual of the confinement/deconfinement transition
in terms of a Gregory-Laflamme transition of the AdS soliton in the IIB frame,
where the strong coupling continuation of the deconfinement phase of YM4 is a
localized D3 soliton. Our proposal offers a new explanation of several aspects
of the thermodynamics of holographic QCD. As an example, we show a new
mechanism of chiral symmetry restoration in the Sakai-Sugimoto model. The
issues discussed in this paper pertain to gravity duals of non-supersymmetric
gauge theories in general.
