JWST's TEMPLATES for Star Formation: The First Resolved Gas-Phase Metallicity Maps of Dust-Obscured Star-Forming Galaxies at $z$ $\sim$ 4

We present the first spatially resolved maps of gas-phase metallicity for two dust-obscured star-forming galaxies (DSFGs) at $z\sim$ 4, from the JWST TEMPLATES Early Release Science program, derived from NIRSpec integral field unit spectroscopy of the H$α$ and [NII] emission lines. Empirical optical line calibrations are used to determine that the sources are globally enriched to near-solar levels. While one source shows elevated [NII]/H$α$ ratios and broad H$α$ emission consistent with the presence of an AGN in a $\gtrsim$1kpc region, we argue that both systems have already undergone significant metal enrichment as a result of their extremely high star formation rates. Utilizing ALMA rest-frame 380$μ$m continuum and [CI]($^3$P$_2$-$^3$P$_1$) line maps we compare the spatial variation of the metallicity and gas-to-dust ratio in the two galaxies, finding the two properties to be anticorrelated on highly resolved spatial scales, consistent with various literature studies of $z\sim$ 0 galaxies. The data are indicative of the enormous potential of JWST to probe the enrichment of the interstellar medium on $\sim$kpc scales in extremely dust-obscured systems at $z\sim$ 4 and beyond.