  We present photometric redshift estimates for galaxies used in the weak
lensing analysis of the Dark Energy Survey Science Verification (DES SV) data.
Four model- or machine learning-based photometric redshift methods -- ANNZ2,
BPZ calibrated against BCC-Ufig simulations, SkyNet, and TPZ -- are analysed.
For training, calibration, and testing of these methods, we construct a
catalogue of spectroscopically confirmed galaxies matched against DES SV data.
The performance of the methods is evaluated against the matched spectroscopic
catalogue, focusing on metrics relevant for weak lensing analyses, with
additional validation against COSMOS photo-zs. From the galaxies in the DES SV
shear catalogue, which have mean redshift $0.72\pm0.01$ over the range
$0.3<z<1.3$, we construct three tomographic bins with means of $z=\{0.45, 0.67,
1.00\}$. These bins each have systematic uncertainties $\delta z \lesssim 0.05$
in the mean of the fiducial SkyNet photo-z $n(z)$. We propagate the errors in
the redshift distributions through to their impact on cosmological parameters
estimated with cosmic shear, and find that they cause shifts in the value of
$\sigma_8$ of approx. 3%. This shift is within the one sigma statistical errors
on $\sigma_8$ for the DES SV shear catalog. We further study the potential
impact of systematic differences on the critical surface density,
$\Sigma_{\mathrm{crit}}$, finding levels of bias safely less than the
statistical power of DES SV data. We recommend a final Gaussian prior for the
photo-z bias in the mean of $n(z)$ of width $0.05$ for each of the three
tomographic bins, and show that this is a sufficient bias model for the
corresponding cosmology analysis.
