[C II] luminosity as a function of the rest-frame equivalent width (EW) of Ly-α. Hot DOGs are displayed as red squares. Normal star-forming galaxies at z ∼ 4−6 are shown as pink diamonds (Le Fèvre et al. 2020). The sample of Ly-α emitters (LAEs) at z ≃ 5−7 from Harikane et al. (2018) are displayed as gray circles, together with the fit to the correlation they found using the Ly-α EW corrected for inter-galactic medium absorption (their Eq. (25)). While we do not attempt such a correction in our sample of luminous Hot DOGs, the average increase in the EW of LAEs due to this effect is less than a factor of two. Hot DOGs deviate from the correlation by more than one order of magnitude, toward larger L_[C II] for a given Ly-α (or vice versa). The arrows indicate a proportionally equal increase in the luminosity of both emission lines by a factor of 10 and 500 from the correlation toward W0134–2922 and W2246–052, and toward W0220+0137 and W0831–0140, respectively.