Holographic Unified Electrodynamics: Derivation of Maxwell Equations and Dark Energy from Topological Charges on the Cosmological Horizon

We address a fundamental question in theoretical physics: how do gauge theories and dark energy emerge from a holographic framework of gravity? We demonstrate that 4D electrodynamics and dark energy with equation of state w ≈ -1 simultaneously arise from the surface thermodynamics of the cosmological apparent horizon decorated with topological U(1) Chern numbers. We rigorously derive Maxwell's equations from a 2+1D surface Chern-Simons action via a UV-regularized bulk-to-boundary propagator. Dark energy emerges naturally as negative holographic surface tension. We provide a parameter-free prediction for the coupling β = α_em / (8π²) and propose five falsifiable observational tests including CMB V-mode polarization, FRB time delays, and running of α_em. This work suggests a unified origin for electromagnetism and cosmic acceleration