  We present new accurate measurements of the physical properties of a
statistically significant sample of 103 galaxies at z~2 using near-infrared
spectroscopy taken as part of the 3D-HST survey. We derive redshifts,
metallicities and star formation rates (SFRs) from the [OII], [OIII] and Hbeta
nebular emission lines and exploit the multi-wavelength photometry available in
CANDELS to measure stellar masses. We find the mass-metallicity relation (MZR)
derived from our data to have the same trend as previous determinations in the
range 0<z<3, with lower mass galaxies having lower metallicities. However we
find an offset in the relation compared to the previous determination of the
z~2 MZR by Erb et al. 2006b, who measure metallicities using the [NII]/Halpha
ratio, with metallicities lower at a given mass. Incorporating our SFR
information we find that our galaxies are offset from the Fundamental
Metallicity Relation (FMR) by ~0.3 dex. We investigate the photoionization
conditions and find that our galaxies are consistent with the elevated
ionization parameter previously reported in high-redshift galaxies. Using the
BPT diagram we argue that, if this is the case, metallicity indicators based on
[NII] and Halpha may not be consistent with the ones obtained via oxygen lines
and Hbeta. Using a recent determination of the theoretical evolution of the
star forming sequence in the BPT diagram we convert our measured [OIII]/Hbeta
line ratios to [NII]/Halpha ratios. From the [NII]/Halpha ratio we infer
systematically higher metallicities in better agreement with the FMR. Our
results thus suggest the evolution of the FMR previously reported at z~2-3 may
be an artifact of the differential evolution in metallicity indicators, and
caution against using locally calibrated metallicity relations at high redshift
which do not account for evolution in the physical conditions of star-forming
regions.
