We present ultraviolet through near-infrared photometry and spectroscopy of the host galaxies of all superluminous supernovae (SLSNe) discovered by the Palomar Transient Factory prior to 2013, and derive measurements of their luminosities, star-formation rates, stellar masses, and gas-phase metallicities. We find that Type I (hydrogen-poor) SLSNe are found almost exclusively in low-mass (M < 2x10^9 M_sun) and metal-poor (12+log[O/H] < 8.4) galaxies. We compare the mass and metallicity distributions of our sample to nearby galaxy catalogs in detail and conclude that the rate of SLSNe-I as a fraction of all SNe is heavily suppressed in galaxies with metallicities >0.5 Z_sun. Extremely low metallicities are not required, and indeed provide no further increase in the relative SLSN rate. Several SLSN-I hosts are undergoing vigorous starbursts, but this may simply be a side effect of metallicity dependence: dwarf galaxies tend to have bursty star-formation histories. Type-II (hydrogen-rich) SLSNe are found over the entire range of galaxy masses and metallicities, and their integrated properties do not suggest a strong preference for (or against) low-mass/low-metallicity galaxies. Two hosts exhibit unusual properties: PTF 10uhf is a Type I SLSN in a massive, luminous infrared galaxy at redshift z=0.29, while PTF 10tpz is a Type II SLSN located in the nucleus of an early-type host at z=0.04.
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