Chiral symmetry of SYM theory in hyperbolic space at finite temperature

We study a holographic gauge theory living in the AdS4 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 cosmological constant (λ) and the dark radiation (C) respectively. The theory studied here is in the confining and chiral symmetry broken phase for λ<0 and small C. When C is increased, the transition to the deconfinement phase has been observed at a finite value of C/|λ|. It is shown here that the chiral symmetry is still broken for a finite range of C/|λ| in the deconfinement phase. In other words, the chiral phase transition occurs at a larger value of C/|λ| than that 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 are compared with a linear sigma model. Furthermore, the entanglement entropy is examined to search for a sign of the chiral phase transition. Several comments are given for these analyses.