Radial distribution of charge-conjugation breaking away from the rotation axis

Characterize the radial distribution of charge-conjugation breaking away from the rotation axis in imaginarily rotating hot QCD, beyond the one-loop analysis restricted to \(r=0\).

Background

The one-loop phase-structure analysis in the paper is restricted to the rotation axis, where the effective potential depends only on the imaginary angular velocity. Away from the axis, the potential also depends on the dimensionless radial coordinate $\tilde r=rT$. Although the exact mapping at $\tilde\Omega_I=2\pi$ applies throughout the system, the spatial radial profile of the charge-conjugation-breaking phase is not determined.