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A search for long-lived particles decaying into displaced electrons and/or muons with large impact parameters is presented. This signature provides unique sensitivity to the production of theoretical supersymmetric lepton-partners, sleptons, with lifetimes between 0.01 and 10 ns. This search is done for the first time at the Large Hadron Collider (LHC), and covers a long-standing gap in coverage of possible new physics signatures. The search is performed using 139 fb^-1 of sqrt{s} = 13 TeV proton-proton collision data collected by the ATLAS detector at the LHC between 2015 and 2018. Special reconstruction and identification algorithms are used to efficiently select leptons with large impact parameters. Backgrounds are estimated from data. Results are consistent with background, and so limits on slepton masses and lifetimes in this model are calculated at 95% CL. For 0.1 ns lifetimes selectron, smuon and stau masses up to 720 GeV, 680 GeV, and 340 GeV are excluded, respectively, drastically improving on the previous best limits from LEP.




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