Abstract
This thesis presents a search for events in a final state containing two opposite-sign, same-flavor leptons, two isolated photons, and significant missing transverse momentum. The final state signature is motivated by slepton pair-production in models describing extensions to the Minimal Supersymmetric Standard Model, with sleptons decaying to a neutralino and lepton, and neutralinos decaying to a photon and one of two supersymmetric particles---the massless, true goldstino and the massive pseudo-goldstino. This work is a novel analysis and is performed with the full Run-II ATLAS dataset, consisting of 139 inverse femtobarns of proton-proton collision data, at a center-of-mass energy of 13 TeV. No significant excess is observed, and results are presented as exclusion limits at the 95% confidence level as a function of the neutralino-to-pseudo-goldstino branching ratio for each signal sample.