Analytical Structure and Spectroscopic Signatures of Quartic Nonlinear Electrodynamics in Holographic Fermion Systems
We investigate the effects of the leading string-inspired quartic correction $α'^2F^4$ on holographic fermions and charge transport in a bottom-up AdS$_4$/CFT$_3$ model. Working in the probe limit, we derive the nonlinear electrostatic background, obtain an exact first integral of the gauge equation, establish the associated constitutive relation, and identify the endpoint of the globally regular electrostatic branch. A nonlinear response function naturally emerges from the gauge sector and provides a unified description of the background, gauge-field fluctuations, and transport coefficients. Using these analytical backgrounds, we compute the fermionic retarded Green's function and spectral function. The quartic interaction shifts the Fermi momentum, enhances the spectral weight, increases the renormalized Fermi velocity, and reduces both momentum and energy linewidths, providing spectroscopic signatures consistent with enhanced quasiparticle coherence while preserving the holographic Fermi surface. We further investigate optical and DC conductivities, showing that the nonlinear interaction redistributes the optical response from the infrared toward intermediate frequencies, whereas the DC conductivity is obtained analytically as $σ_{\mathrm{DC}}=\mathcal K(1)=ρ/E(1)$ and decreases monotonically with increasing nonlinear coupling. These results establish a direct connection between nonlinear bulk electrodynamics, momentum-resolved spectroscopic observables, and transport properties in the dual strongly coupled theory.