N=2 supersymmetric Yang-Mills theory with flavor hypermultiplets at finite
temperature and in the dS4β are studied for finite quark number density
(nbβ) by a dual supergravity background with non-trivial dilaton and axion.
The quarks and its number density nbβ are introduced by embedding a probe D7
brane. We find a critical value of the chemical potential at the limit of
nbβ=0, and it coincides with the effective quark mass given in each theory
for nbβ=0. At this point, a transition of the D7 embedding configurations
occurs between their two typical ones. The phase diagrams of this transition
are shown in the plane of chemical potential versus temperature and
cosmological constant for YM theory at finite temperature and in dS4β
respectively. In this phase transition, the order parameter is considered as
nbβ. % and the critical value of the chemical potential This result seems to
be reasonable since both theories are in the quark deconfinement phase.Comment: 17 pages, 8 figure