Subregion complexity and confinement-deconfinement transition in a holographic QCD model

Abstract: We study the subregion complexity in a semi-analytical holographic QCD model. Two cases with different warped factor are considered and both can realize confinement-deconfinement transition. By studying the behavior of the renormalized holographic complexity density $\hat{\cal C}$ versus the subregion length scale $\ell$, we find that for both cases, $\hat{\cal C}$ always experiences a discontinuity at certain critical value $\ell_c$ in confinement phases, while it is always continuous in deconfinement phases. This property may be seen as a signal to characterize confinement or deconfinement phases. The behavior of $\hat{\cal C}$ versus the temperature and chemical potential is also investigated and our results show that $\hat{\cal C}$ exhibits behavior characterizing the type of the transition. That is, it experiences a discontinuity at the transition temperature for $\mu < \mu_c$ where first-order confinement-deconfinement phase transition happens, while it is always continuous for $\mu> \mu_c$ where the transition turns into a turnover. These results imply that the renormalized holographic complexity density may be used as a good parameter to characterize the corresponding phase structures.