Direct photon production at mid-rapidity in Pb–Pb collisions at d="mmlsi1" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000320&_mathId=si1.gif&_user=111111111&_pii=S0370269316000320&_rdoc=1&_issn=03702693&md5=1c8185232f9746b818569f8c750d7a2c">dth="105" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316000320-si1.gif">dden">de"> was studied in the transverse momentum range d="mmlsi148" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000320&_mathId=si148.gif&_user=111111111&_pii=S0370269316000320&_rdoc=1&_issn=03702693&md5=0013d3c9759dbd106f0bce3f81d2dae8" title="Click to view the MathML source">0.9<pT<14 GeV/cdden">de">. Photons were detected with the highly segmented electromagnetic calorimeter PHOS and via conversions in the ALICE detector material with the d="mmlsi4" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000320&_mathId=si4.gif&_user=111111111&_pii=S0370269316000320&_rdoc=1&_issn=03702693&md5=1166737fefdecce3d6290006e66f4e08" title="Click to view the MathML source">e+e−dden">de"> pair reconstructed in the central tracking system. The results of the two methods were combined and direct photon spectra were measured for the 0–20%, 20–40%, and 40–80% centrality classes. For all three classes, agreement was found with perturbative QCD calculations for d="mmlsi5" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000320&_mathId=si5.gif&_user=111111111&_pii=S0370269316000320&_rdoc=1&_issn=03702693&md5=f876eeae8231e04158b538b59eb9bcfd" title="Click to view the MathML source">pT≳5 GeV/cdden">de">. Direct photon spectra down to d="mmlsi6" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000320&_mathId=si6.gif&_user=111111111&_pii=S0370269316000320&_rdoc=1&_issn=03702693&md5=145471da8223133907c91fcc1011f6da" title="Click to view the MathML source">pT≈1 GeV/cdden">de"> could be extracted for the 20–40% and 0–20% centrality classes. The significance of the direct photon signal for d="mmlsi7" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000320&_mathId=si7.gif&_user=111111111&_pii=S0370269316000320&_rdoc=1&_issn=03702693&md5=4067fc100418e5d9dc8ef576fcc34c21" title="Click to view the MathML source">0.9<pT<2.1 GeV/cdden">de"> is 2.6σ for the 0–20% class. The spectrum in this d="mmlsi8" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000320&_mathId=si8.gif&_user=111111111&_pii=S0370269316000320&_rdoc=1&_issn=03702693&md5=aa58cb03581d230341ba1ff810fef8b0" title="Click to view the MathML source">pTdden">de"> range and centrality class can be described by an exponential with an inverse slope parameter of d="mmlsi9" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000320&_mathId=si9.gif&_user=111111111&_pii=S0370269316000320&_rdoc=1&_issn=03702693&md5=2e8066a435697eed598476449755381f" title="Click to view the MathML source">(297±12stat±41syst) MeVdden">de">. State-of-the-art models for photon production in heavy-ion collisions agree with the data within uncertainties.