  We study the gravity dual of four dimensional pure Yang-Mills theory through
D4 branes, as proposed by Witten (holographic QCD). In this holographic QCD, it
has been widely believed that the confinement phase in the pure Yang-Mills
theory corresponds to the AdS D4 soliton in gravity and the deconfinement phase
corresponds to the black D4 brane. We inspect this conjecture carefully and
show that the correspondence between the black D4 brane and the deconfinement
phase is not correct. Instead, by using a slightly different set up, we find an
alternative gravity solution called "localized soliton", which would be
properly related to the deconfinement phase. In this case, the
confinement/deconfinement transition is realized as a Gregory-Laflamme type
transition. We find that our proposal naturally explains several known
properties of QCD.

High Energy Physics - Theory;High Energy Physics - Lattice;High Energy Physics - Phenomenology