We present the first results of our spectroscopic follow-up of 6.5 < z < 10 candidate galaxies behind clusters of galaxies. We report the spectroscopic confirmation of an intrinsically faint Lyman break galaxy (LBG) identified as a z 850LP-band dropout behind the Bullet Cluster. We detect an emission line at {lambda} = 9412 {AA} at >5{sigma} significance using a 16 hr long exposure with FORS2 VLT. Based on the absence of flux in bluer broadband filters, the blue color of the source, and the absence of additional lines, we identify the line as Ly{alpha} at z = 6.740 pm 0.003. The integrated line flux is f = (0.7 pm 0.1 pm 0.3) times 10^{-17} erg^{-1} s^{-1} cm^{-2} (the uncertainties are due to random and flux calibration errors, respectively) making it the faintest Ly{alpha} flux detected at these redshifts. Given the magnification of {mu} = 3.0 pm 0.2 the intrinsic (corrected for lensing) flux is f^int = (0.23 pm 0.03 pm 0.10 pm 0.02) times 10^{-17} erg^{-1} s^{-1} cm^{-2} (additional uncertainty due to magnification), which is ~2-3 times fainter than other such measurements in z ~ 7 galaxies. The intrinsic H 160W-band magnitude of the object is m^int(H_160W)=27.57 pm 0.17, corresponding to 0.5 L* for LBGs at these redshifts. The galaxy is one of the two sub-L* LBG galaxies spectroscopically confirmed at these high redshifts (the other is also a lensed z = 7.045 galaxy), making it a valuable probe for the neutral hydrogen fraction in the early universe.
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