  We investigate the dimensional dependence (D-dependence) of the difference
(gap) between the critical temperatures associated with the uniform/non-uniform
and non-uniform/gapped transitions in the large-N bosonic gauge theories with D
matrix scalar fields on a circled space. We use the equations describing these
critical temperatures given in the 1/D expansion arXiv:0910.4526. These
transitions are related with Gregory-Laflamme instabilities in the gravities
and Rayleigh-Plateau instabilities in the fluid dynamics, and qualitative
similarities between these are expected. We find that the tendency in the
D-dependence of the gap is opposite from those in the gravity and fluid side.
This is interesting as a counterexample to the gauge/gravity and gauge/fluid
correspondences.
