Researchers have investigated the interactions between static quark-antiquark pairs within a rotating gluonic medium, utilizing lattice Quantum Chromodynamics (QCD) simulations. The study was conducted at imaginary angular velocity, a technique that allows for the exploration of rotating systems without the complexities of real-time dynamics. The static potential at zero temperature and free energies at finite temperature were examined, analyzing how these fundamental interactions are influenced by rotation across various geometric configurations of the quarks.

At zero temperature, the static potential was extracted from Wilson loops for quark-antiquark pairs aligned with the rotation axis, as well as for transverse pairs. The results indicate that, within the current simulation accuracy, no significant rotation dependence or anisotropy was observed in the static potential. This suggests that, in the absence of thermal effects, the strong interaction between quarks is not appreciably altered by the rotation of the gluonic medium.

At finite temperature, above the deconfinement temperature ($T_c$), imaginary rotation suppresses the color-averaged free energies, which were obtained from Polyakov-loop correlators. This suppression is evident in both longitudinal and transverse geometries. In the bulk region of the system, the large-distance longitudinal free-energy shift is well described by a quadratic relationship with the transverse distance ($ΔF_z(R_{xy})=A R_{xy}^2+B$). The transverse channels exhibit a qualitatively similar suppression, with a distance dependence that reflects the radial arrangement of the static sources. As the temperature increases above $T_c$, the response to rotation weakens, indicating a reduced sensitivity of the hot medium to this effect.

These findings provide lattice evidence for a position- and geometry-dependent response of bare static-source free energies to imaginary rotation in a gluonic medium. This work contributes to a better understanding of the properties of quark-gluon matter under extreme conditions, such as those found in the interiors of neutron stars or in heavy-ion collisions, where rotating states of the quark-gluon plasma are generated.