In this work we formulate an information–gauge completion of a renormalizable entanglement/entropy-based effective field theory by promoting coarse-grained local entropy (information) flow to an Abelian gauge sector with a single ultralight vector field. A gauge-invariant mass is implemented through a Stückelberg phase, yielding a BRST-consistent, power-counting renormalizable truncation that is suitable for real-time functional renormalization group (FRG) analysis. A central conceptual point—often glossed over in related constructions—is that the entropic current in our framework is operational (Schwinger–Keldysh/coarse-grained) rather than a Noether charge current, and is therefore generically nonconserved off shell. We show explicitly that the Stückelberg completion reorganizes the coupling to a nonconserved current into a controlled scalar source: the nonconservation couples only to the Stückelberg scalar, while the transverse vector couples to the conserved component. This yields a transparent EFT validity criterion and a high-energy perturbative unitarity bound. On the infrared side, the real-time FRG flow generates a small but finite time–space anomalous-dimension splitting in the entropy-deformed sector, leading to a modified pseudo-Goldstone damping law. We further provide explicit UV→IR matching routes for the parity-odd mixing relevant to cosmic birefringence: we clarify that the constant-coefficient term is a total derivative producing no bulk rotation, and we show how an observable axion-like portal can emerge via (i) dynamical coefficient dependence or (ii) heavy-threshold matching. This produces a self-contained set of correlated signatures connecting fifth-force constraints, FRG-induced damping anomalies, and cosmic birefringence.
Ju Hyung Lee (Tue,) studied this question.