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This letter documents a search for flavour-changing neutral currents (FCNCs),which are strongly suppressed in the Standard Model, in events with a photonand a top quark with the ATLAS detector. The analysis uses data collected in$pp$ collisions at $\sqrt{s} = 13$ TeV during Run 2 of the LHC, correspondingto an integrated luminosity of 139 fb$^{-1}$. Both FCNC top-quark productionand decay are considered. The final state consists of a charged lepton, missingtransverse momentum, a $b$-tagged jet, one high-momentum photon and possiblyadditional jets. A multiclass deep neural network is used to classify eventseither as signal in one of the two categories, FCNC production or decay, or asbackground. No significant excess of events over the background prediction isobserved and 95% CL upper limits are placed on the strength of left- andright-handed FCNC interactions. The 95% CL bounds on the branching fractionsfor the FCNC top-quark decays, estimated from both top-quark production anddecay, are $\mathcal{B}(t\rightarrow u\gamma) < 0.85 \times 10^{-5}$ and$\mathcal{B}(t\to c\gamma) < 4.2 \times 10^{-5}$ for a left-handed $tq\gamma$coupling, and $\mathcal{B}(t\to u\gamma) < 1.2 \times 10^{-5}$ and$\mathcal{B}(t\to c\gamma) < 4.5 \times 10^{-5}$ for a right-handed coupling.

Search for flavour-changing neutral-current couplings between the top quark and the photon with the ATLAS detector at $\sqrt{s} = 13$ TeV