  Current emission-line based estimates of the metallicity of active galactic
nuclei (AGN) at both high and low redshifts indicate that AGN have
predominantly solar to supersolar metallicities. This leads to the question: do
low metallicity AGN exist? In this paper we use photoionization models to
examine the effects of metallicity variations on the narrow emission lines from
an AGN. We explore a variety of emission-line diagnostics that are useful for
identifying AGN with low metallicity gas. We find that line ratios involving
[NII] are the most robust metallicity indicators in galaxies where the primary
source of ionization is from the active nucleus. Ratios involving [SII] and
[OI] are strongly affected by uncertainties in modelling the density structure
of the narrow line clouds. To test our diagnostics, we turn to an analysis of
AGN in the Sloan Digital Sky Survey (SDSS). We find a clear trend in the
relative strength of [NII] with the mass of the AGN host galaxy. The
metallicity of the ISM is known to be correlated with stellar mass in
star-forming galaxies; our results indicate that a similar trend exists for
AGN. We also find that the best-fit models for typical Seyfert narrow line
regions have supersolar abundances. Although there is a mass-dependent range of
a factor of 2-3 in the NLR metallicities of the AGN in our sample, AGN with
sub-solar metallicities are very rare in the SDSS. Out of a sample of ~23000
Seyfert 2 galaxies we find only ~40 clear candidates for AGN with NLR
abundances that are below solar.
