$N=2$ supersymmetric Yang-Mills theory with flavor hypermultiplets at finite temperature and in the ${\mathrm{dS}}_4$ space is studied for finite quark number density ($n_b$) by a dual supergravity background with nontrivial dilaton and axion. The quarks and their number density $n_b$ are introduced by embedding a probe D7 brane. We find a critical value of the chemical potential at the limit of $n_b=0$, and it coincides with the effective quark mass given in each theory for $n_b=0$. 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 Yang-Mills theory at finite temperature and in ${\mathrm{dS}}_4$, respectively. In this phase transition, the order parameter is considered as $n_b$. This result seems to be reasonable since both theories are in the quark deconfinement phase.

• Received 2 September 2007

DOI:https://doi.org/10.1103/PhysRevD.76.124006