  We present photometric redshifts (photo-$z$) for the deep wide fields of the
Physics of the Accelerating Universe Survey (PAUS), covering an area of
$\sim$50 deg$^{2}$, for $\sim$1.8 million objects up to $i_{\textrm{AB}}<23$.
The PAUS deep wide fields overlap with the W1 and W3 fields from CFHTLenS and
the G09 field from KiDS/GAMA. Photo-$z$ are estimated using the 40 narrow bands
(NB) of PAUS and the broad bands (BB) of CFHTLenS and KiDS. We compute the
redshifts with the SED template-fitting code BCNZ, with a modification in the
calibration technique of the zero-point between the observed and the modelled
fluxes, that removes any dependence on spectroscopic redshift samples. We
enhance the redshift accuracy by introducing an additional photo-$z$ estimate
($z_{\textrm{b}}$), obtained through the combination of the BCNZ and the
BB-only photo-$z$. Comparing with spectroscopic redshifts estimates
($z_{\textrm{s}}$), we obtain a $\sigma_{68} \simeq 0.019$ for all galaxies
with $i_{\textrm{AB}}<23$ and a typical bias $|z_{\textrm{b}}-z_{\textrm{s}}|$
smaller than 0.01. For $z_{\textrm{b}} \sim (0.10-0.75)$ we find $\sigma_{68}
\simeq (0.003-0.02)$, this is a factor of $10-2$ higher accuracy than the
corresponding BB-only results. We obtain similar performance when we split the
samples into red (passive) and blue (active) galaxies. We validate the redshift
probability $p(z)$ obtained by BCNZ and compare its performance with that of
$z_{\textrm{b}}$. These photo-$z$ catalogues will facilitate important science
cases, such as the study of galaxy clustering and intrinsic alignment at high
redshifts ($z \lesssim 1$) and faint magnitudes.
