The Nature of 500 micron Risers I: SMA Observations.

We present SMA observations at resolutions from 0.35 to 3 arcseconds of a sample of 34 candidate high redshift dusty star forming galaxies (DSFGs). These sources were selected from the HerMES Herschel survey catalogues to have SEDs rising from 250 to 350 to 500$\mu$m, a population termed 500-risers. We detect counterparts to 24 of these sources, with four having two counterparts. We conclude that the remaining ten sources that lack detected counterparts are likely to have three or more associated sources which blend together to produce the observed Herschel source. We examine the role of lensing, which is predicted to dominate the brightest (F500 $>$ 60mJy) half of our sample. We find that while lensing plays a role, at least 35% of the bright sources are likely to be multiple sources rather than the result of lensing. At fainter fluxes we find a blending rate comparable to, or greater than, the predicted 40%. We determine far-IR luminosities and star formation rates for the non-multiple sources in our sample and conclude that, in the absence of strong lensing, our 500-risers are very luminous systems with L$_{FIR} > 10^{13}$L$_{\odot}$ and star formation rates $> 1000$M$_{\odot}$/yr.