Chromomagnetic condensation and perturbative confinement induced by imaginary rotation in SU(2) Yang-Mills Theory

We perturbatively investigate the rotation effect on the Polyakov loop potential in SU(2) gauge theroy within a chromomagnetic background. It is observed that the imaginary rotation spontaneously induces both confinement and chromomagnetic condensation at high temperatures, thereby provides a perturbative window to explore non-perturbative dynamics. Compared to the case without including the induced chromomagnetic field, the perturbative confinement transition becomes first-order, with a temperature-dependent phase boundary that asymptotically approaches $\tildeΩ_c = π/\sqrt{3}$ at high temperatures. This leads to a significantly enriched $\tildeΩ$-$T$ phase diagram characterized by an expanded deconfined region. For real angular velocities, we find that the chromomagnetic condensate decreases with increasing rotation, and that the coupling between rotation, spin, and the chromomagnetic background leads to a cusp in the Polyakov loop potential, suggesting that the underlying dynamics could be more intricate.