Chiral Symmetry of SYM theory in hyperbolic space at finite temperature

We study a holographic gauge theory living in the AdS$_4$ space-time at finite temperature. The gravity dual is obtained as a solution of the type IIB superstring theory with two free parameters, which correspond to four dimensional (4D) cosmological constant ($\lambda$) and the dark radiation ($C$) respectively. The theory studied here is in confining and chiral symmetry broken phase for $\lambda <0$ and small $C$. When $C$ is increased, the transition to the deconfinement phase has been observed at a finite value of $C/|\lambda|$. It is shown here that the chiral symmetry is still broken for a finite range of $C/|\lambda|$ in the deconfinement phase. In other words, the chiral phase transition occurs at a larger value of $C/|\lambda|$ than the one of the deconfinement transition. So there is a parameter range of a new deconfinement phase with broken chiral symmetry. In order to study the properties of this phase, we performed a holographic analysis for the meson mass-spectrum and other quantities in terms of the probe D7 brane. The results of this analysis are compared with a linear sigma model. Furthermore, the entanglement entropy is examined to search for a sign of the chiral phase trantion. Several comments are given for these analyses.