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We have used the IRAM Plateau de Bure mm interferometer to locate withsubarcsecond accuracy the dust emission of three of the brightest 1.2mm sourcesin the NTT Deep Field (NDF) selected from our 1.2mm MAMBO survey at the IRAM30m telescope. We combine these results with deep B to K imaging and VLAinterferometry. Strikingly, none of the three accurately located mm galaxiesMMJ120546-0741.5, MMJ120539-0745.4, and MMJ120517-0743.1 has a K-bandcounterpart down to the faint limit of K>21.9. This implies that these threegalaxies are either extremely obscured and/or are at very high redshifts(z>~4). We combine our results with literature data for 11 more (sub)mmgalaxies that are identified with similar reliability. In terms of their K-bandproperties, the sample divides into three roughly equal groups: (i) undetectedto K~22, (ii) detected in the near-infrared but not the optical and (iii)detected in the optical with the possibility of optical follow-up spectroscopy.We find a trend in this sample between near-infrared to submm and submm toradio spectral indices, which in comparison to spectral energy distributions(SEDs) of low redshift infrared luminous galaxies suggests that the mostplausible primary factor causing the extreme near-infrared faintness of ourobjects is their high redshift. We show that the near-infrared to radio SEDs ofthe sample are inconsistent with SEDs that resemble local far-infrared coolgalaxies with moderate luminosities, which were proposed in some models of thesubmm sky. We briefly discuss the implications of the results for ourunderstanding of galaxy formation.Comment: aastex, 5 figures. Accepted by Ap

Properties of Millimeter Galaxies: Constraints fromK‐Band Blank Fields