[en] We present a comprehensive first-principles investigation of the electronic and optical properties of CsK₂Sb, a semiconducting material for ultra-bright electron sources for particle accelerators. Our study, based on density-functional theory and many-body perturbation theory, provides all the ingredients to model the emission of this material as a photocathode, including band gap, band dispersion, and optical absorption. An accurate description of these properties beyond the mean-field picture is relevant to take into account many-body effects. We discuss our results in the context of state-of-the-art electron sources for particle accelerators to set the stage towards improved modeling of quantum efficiency, intrinsic emittance, and other relevant quantities determining the macroscopic characteristics of photocathodes for ultra-bright beams. (paper)