We present the properties of active galactic nuclei (AGN) selected by optical variability in the Subaru/XMM-Newton Deep Field (SXDF). Based on the locations of variable components and light curves, 211 optically variable AGN were reliably selected. We made three AGN samples; X-ray detected optically non-variable AGN (XA), X-ray detected optically variable AGN (XVA), and X-ray undetected optically variable AGN (VA). In the VA sample, we found a bimodal distribution of the ratio between the variable component flux and the host flux. One of these two components in the distribution, a class of AGN with a faint variable component $i_{rm{vari}}sim25$ mag in bright host galaxies $isim21$ mag, is not seen in the XVA sample. These AGN are expected to have low Eddington ratios if we naively consider a correlation between bulge luminosity and black hole mass. These galaxies have photometric redshifts $z_{rm{photo}}sim0.5$ and we infer that they are low-luminosity AGN with radiatively inefficient accretion flows (RIAFs). The properties of the XVA and VA objects and the differences from those of the XA objects can be explained within the unified scheme for AGN. Optical variability selection for AGN is an independent method and could provide a complementary AGN sample which even deep X-ray surveys have not found.
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