Perturbative Confinement in Thermal Yang-Mills Theories Induced by Imaginary Angular Velocity

We perturbatively compute the Polyakov loop potential at high temperature with finite imaginary angular velocity. This imaginary rotation does not violate the causality, and the thermodynamic limit is well defined. We analytically show that the imaginary angular velocity induces the perturbatively confined phase and serves as a new probe to confinement physics. We discuss a possible phase diagram that exhibits adiabatic continuity from the perturbative confinement to the confined phase at low temperature. We also mention subtlety in the analytical continuation from imaginary to real angular velocity by imposing a causality bound.

Automated summary

In this study, the Polyakov loop potential at high temperature with finite imaginary angular velocity is computed perturbatively. It is demonstrated analytically that the imaginary angular velocity induces the perturbatively confined phase, serving as a new approach to investigate confinement physics. Moreover, a possible phase diagram is discussed, showing adiabatic continuity from perturbative confinement to the confined phase at low temperature, and a subtle point is mentioned regarding the analytical continuation from imaginary to real angular velocity by imposing a causality bound.