Phase transition of QCD under rotation and revisit from a bag model

In this talk, I review the recent theoretical developments in the QCD thermodynamics under an external rotation. Followed by brilliant experimental measurements of a strong vorticity in QGP, a crucial task on the theoretical side is to reveal the vortical or rotational effect on quantum field theory. For the past few years, especially, various model approaches elucidated that rotation favors both chiral restoration and deconfinement. On the other hand, the first principle lattice QCD simulation cannot be directly applied to rotating systems, due to the sign problem. Nevertheless, some simulations with an imaginary angular velocity indicate an inconsistent result with the model prediction, although an issue about an analytic structure would be involved in the lattice simulation itself. To clarify such a gap between the model approaches and lattice simulation, I revisit the deconfinement transition based on the bag model under rotation. I demonstrate that the transition temperature becomes an increasing (decreasing) function of angular velocity, if we do (do not) take into account the revolution effect of the confinement potential. This result implies that the correction to the QCD interactions would be an overlooked but crucial ingredient to determine the thermodynamics of rotating quark and gluons.