This manuscript computes the one-loop beta-function coefficient for a GL (k, C) gauge theory deformed by a non-Hermitian mixing parameter. We demonstrate that the Faddeev-Popov ghost contribution vanishes exactly, and a remarkable cancellation in the cross-heat-kernel trace yields a purely universal, rank-independent coefficient C₁ = -2/11 for all k >= 2. Consequently, we derive the exact closed-form expression for the critical mixing parameter, below which asymptotic freedom is robustly preserved. Furthermore, we prove that the biorthogonal wavefunction renormalisation product remains strictly real and positive within this asymptotically free regime, guaranteeing the stability of the conserved information charge under renormalization-group flow. These results establish the ultraviolet consistency of non-Hermitian gauge theories with mixing.
Chao Ma (Sat,) studied this question.