On the nature of infrared-faint radio sources in the SXDF and VLA-VVDS
  fields
  Infrared-Faint Radio Sources (IFRSs) are an unusual class of objects that are
relatively bright at radio wavelengths but have faint or undetected infrared
counterparts even in deep surveys. We identify and investigate the nature of
IFRSs using deep radio (S$_{\rm 1.4~GHz}$ $\sim$ 100 $\mu$Jy beam$^{-1}$ at
5$\sigma$), optical (m$_{\rm r}$ $\sim$ 26 - 27.7 at 5$\sigma$), and near-IR
(S$_{\rm 3.6~{\mu}m}$ $\sim$ 1.3 - 2.0 $\mu$Jy beam$^{-1}$ at 5$\sigma$) data
available in two deep fields namely the Subaru X-ray Deep Field (SXDF) and the
Very Large Array - VIMOS VLT Deep Survey (VLA-VVDS) field. In 1.8 deg$^{2}$ of
the two fields we identify a total of nine confirmed and ten candidate IFRSs.
We find that our IFRSs are high-redshift radio-loud AGN, with 12/19 sources
having redshift estimates in the range of $z$ $\sim$ 1.7 - 4.3, while a limit
of $z$ $\geq$ 2.0 is placed for the remaining seven sources. Notably, our study
finds, for the first time, IFRSs with measured redshift $>$ 3.0, and also, the
redshift estimates for IFRSs in the faintest 3.6 $\mu$m flux regime i.e.,
S$_{\rm 3.6~{\mu}m}$ $<$ 1.3 ${\mu}$Jy. Radio observations show that our IFRSs
exhibit both compact unresolved as well as extended double-lobe morphologies,
and have predominantly steep radio spectra between 1.4 GHz and 325 MHz. The
non-detection of all but one IFRSs in the X-ray band and the optical-to-MIR
colour (m$_{\rm r}$ - m$_{\rm 24~{\mu}m}$) suggest that a significant fraction
of IFRSs are likely to be hosted in dusty obscured galaxies.
