Energy-minimizing alignment of generated magnetic field with rotation axis in a rotating frame

Establish whether, in the co-moving frame of a steady mechanical rotation with angular velocity vector Ω = Ω ẑ, the energetically favored configuration of any spontaneously generated magnetic field is parallel to the rotation axis (B = B ẑ) within the chiral perturbation theory setup considered for rotating nuclear matter.

Background

The paper analyzes baryonic vortices in rotating nuclear matter within chiral perturbation theory, allowing for dynamical electromagnetism and the Wess–Zumino–Witten term. In setting up the rotating background, the authors posit by symmetry that any generated magnetic field should align with the rotation axis, which they describe as a natural conjecture.

They subsequently adopt a gauge configuration A = A_φ(ρ) dφ consistent with a magnetic field along the rotation axis. Verifying that the energy minimum indeed occurs for B parallel to the rotation axis would substantiate this foundational modeling assumption and clarify whether alternative orientations could be energetically competitive in the same framework.