D-dependence of the gap between the critical temperatures in the one-dimensional gauge theories

Abstract

Abstract 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 $$S^1$$ S1 -circled space. We use the equations describing these critical temperatures given in the 1/D expansion Mandal et al. (JHEP 1002:034, 2010). These transitions are related with the Gregory-Laflamme instabilities in the gravities and the 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.