The maximum luminosity of fast radio bursts

Under the assumption that fast radio bursts (FRBs) are from coherent curvature emission powered by the dissipation of magnetic energy in the magnetosphere of neutron stars, we predict a maximum isotropic equivalent luminosity of (~2x10^{47} erg/s) min({\rho}^2, B{\rho}^{4/3}{\nu}^{-2/3}), where {\rho} is the curvature radius of the magnetic field lines near the source region in units of 10 km, B is the local magnetic field strength in units of 10^{16} G, and {\nu} is the FRB wave frequency in units of GHz. This is because the electric field responsible for accelerating the radiating particles becomes close to the quantum critical field strength and is then quickly shielded by Schwinger pairs within a nano-second. Future observations should be able to confirm this cut-off luminosity and hence provide a unique probe of the source location and magnetic field strength. We discuss how the maximum luminosity affects the observed flux distributions for repeating bursts from the same object and for the entire FRB population.