Confinement and Pseudoscalar Glueball Spectrum from Anisotropic Non-susy D$2$ Brane under Hawking-Page transition

Here we analyse the low energy confining phase of the $2+1$ dimensional quenched QCD-like theory in anisotropic non-supersymmetric D$2$ brane background with the holographic approach. Two key features of QCD -- flux-tube tension and mass spectrum of pseudoscalar glueball are studied. The non-supersymmetric D$2$ branes with anisotropy in time direction are considered as the gravity theory. Tuning the anisotropic parameter, we get the Hawking-Page transition in the gravity background. On the dual theory, this refers the confinement-deconfinement phase transition. Using the Wilson loop, the linear confinement at this regime is effectively confirmed by calculating the flux tube tension $\sigma$ from the Nambu-Goto action of a test string with its endpoints located at the boundary. In the next part, we have illustrated numerically the mass spectrum $M_{0^{-+}}$ of the pseudoscalar glueball states. We have found, at the transition point, that the glueball mass becomes trivially small. Finally we relate the anisotropy parameter with the temperature and show the variation of the glueball mass at various temperature. Using the Lattice QCD data of $\sqrt{\sigma}$, it is found that $M_{0^{-+}}=2.3$GeV and $M_{0^{-+}}^*=3.8$GeV at $T=0$ whereas $M_{0^{-+}}=0.9$GeV and $M_{0^{-+}}^*=1.1$GeV at $T=T_c$.