  We investigate the existence of a metallicity threshold for the production of
long gamma-ray bursts (LGRBs). We used the host galaxies of the Swift/BAT6
sample of LGRBs. We considered the stellar mass, star formation rate (SFR), and
metallicity determined from the host galaxy photometry and spectroscopy up to z
= 2 and used them to compare the distribution of host galaxies to that of field
galaxies in the mass-metallicity and fundamental metallicity relation plane. We
find that although LGRBs also form in galaxies with relatively large stellar
masses, the large majority of host galaxies have metallicities below
log(O=H)~8.6. The extension to z = 2 results in a good sampling of stellar
masses also above Log(Mstar/Msun)~9.5 and provides evidence that LGRB host
galaxies do not follow the fundamental metallicity relation. As shown by the
comparison with dedicated numerical simulations of LGRB host galaxy population,
these results are naturally explained by the existence of a mild (~0.7 Zsun)
threshold for the LGRB formation. The present statistics does not allow us to
discriminate between different shapes of the metallicity cutoff, but the
relatively high metallicity threshold found in this work is somewhat in
disagreement to most of the standard single-star models for LGRB progenitors.
