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We present our survey for optically faint variable objects using multi-epoch(8-10 epochs over 2-4 years) $i'$-band imaging data obtained with SubaruSuprime-Cam over 0.918 deg$^2$ in the Subaru/XMM-Newton Deep Field (SXDF). Wefound 1040 optically variable objects by image subtraction for all thecombinations of images at different epochs. This is the first statisticalsample of variable objects at depths achieved with 8-10m class telescopes orHST. The detection limit for variable components is $i'_{\rm{vari}}\sim25.5$mag. These variable objects were classified into variable stars, supernovae(SNe), and active galactic nuclei (AGN), based on the optical morphologies,magnitudes, colors, and optical-mid-infrared colors of the host objects,spatial offsets of variable components from the host objects, and light curves.Detection completeness was examined by simulating light curves for periodic andirregular variability. We detected optical variability for $36\pm2%$ ($51\pm3%$for a bright sample with $i'<24.4$ mag) of X-ray sources in the field. Numberdensities of variable obejcts as functions of time intervals $\Delta{t}$ andvariable component magnitudes $i'_{\rm{vari}}$ are obtained. Number densitiesof variable stars, SNe, and AGN are 120, 489, and 579 objects deg$^{-2}$,respectively. Bimodal distributions of variable stars in the color-magnitudediagrams indicate that the variable star sample consists of bright ($V\sim22$mag) blue variable stars of the halo population and faint ($V\sim23.5$ mag) redvariable stars of the disk population. There are a few candidates of RR Lyraeproviding a possible number density of $\sim10^{-2}$ kpc$^{-3}$ at a distanceof $>150$ kpc from the Galactic center.

The Subaru/XMM-Newton Deep Survey (SXDS) - V. Optically Faint Variable Object Survey