  We study the rotation effects of the hot and dense QCD matter in a
non-perturbative regime by the gauge/gravity duality. We use the gravitational
model that is designated to match the state-of-the-art lattice data on the
thermal properties of (2+1)-flavor QCD and predict the location of the critical
endpoint and the first-order phase transition line at large baryon chemical
potential without rotation. After introducing the angular velocity via a local
Lorentz boost, we investigate the thermodynamic quantities for the system under
rotation in a self-consistent way. We find that the critical temperature and
baryon chemical potential associated with the QCD phase transition decrease as
the angular velocity increases. Moreover, some interesting phenomena are
observed near the critical endpoint. We then construct the 3-dimensional phase
diagram of the QCD matter in terms of temperature, baryon chemical potential,
and angular velocity. As a parallel investigation, we also consider the
gravitational model of $SU(3)$ pure gluon system, for which the 2-dimensional
phase diagram associated with temperature and angular velocity has been
predicted. The corresponding thermodynamic quantities with rotation are
investigated.
