Nonperturbative connection between the on-axis transition and the Roberge–Weiss phase structure

Determine nonperturbatively how the on-axis second-order charge-conjugation-breaking transition point connects, at lower temperatures, to the established phase structure on the imaginary-rotation line \(\tilde\Omega_I=2\pi\), while accounting for higher-order and nonperturbative effects that may shift the one-loop transition points and lift the accidental massless one-loop degeneracy.

Background

The paper derives second-order and first-order transition points on the rotation axis using a one-loop effective potential, while establishing an exact correspondence between Ω~I=2π\tilde\Omega_I=2\pi and the Roberge–Weiss point at imaginary quark chemical potential. The authors note that higher-order corrections and nonperturbative effects may modify the one-loop predictions and that the relationship between the on-axis transition and the lower-temperature phase structure on the exact Roberge–Weiss line has not been established.

References

Higher-order corrections and nonperturbative effects may shift the transition points eq:imaginary-rotation-C:critical-angle-Nf3 and eq:imaginary-rotation-C:center-sector-transition and lift the accidental degeneracy of the massless one-loop approximation; how the on-axis second-order point connects, at lower temperatures, to the settled structure on the line \tilde\Omega_I=2\pi is a nonperturbative question.

— Imaginary Rotation Breaks Charge Conjugation in Hot QCD  (2608.25849 - Takada, 26 Aug 2026) in Outlook

In full QCD the degeneracy is thus lifted by a finite s-quark mass, whereas pure Yang-Mills theory has no quark mass to deform it and how its degeneracy is lifted cannot be decided at one loop.

— Imaginary Rotation Breaks Charge Conjugation in Hot QCD  (2608.25849 - Takada, 26 Aug 2026) in Accidental degeneracy of the massless one-loop approximation