The SUperluminous Supernova Host galaxIES (SUSHIES) survey aims to provide
strong new constraints on the progenitors of superluminous supernovae (SLSNe)
by understanding the relationship to their host galaxies. We present the
photometric properties of 53 H-poor and 16 H-rich SLSN host galaxies out to
z∼4. We model their spectral energy distributions to derive physical
properties, which we compare with other galaxy populations. At low redshift,
H-poor SLSNe are preferentially found in very blue, low-mass galaxies with high
average specific star-formation rates. As redshift increases, the host
population follows the general evolution of star-forming galaxies towards more
luminous galaxies. After accounting for secular evolution, we find evidence for
differential evolution in galaxy mass, but not in the B-band and the far UV
luminosity (3σ confidence). Most remarkable is the scarcity of hosts
with stellar masses above 1010M⊙ for both classes of SLSNe. In the
case of H-poor SLSNe, we attribute this to a stifled production efficiency
above ∼0.4 solar metallicity. However, we argue that, in addition to low
metallicity, a short-lived stellar population is also required to regulate the
SLSN production. H-rich SLSNe are found in a very diverse population of
star-forming galaxies. Still, the scarcity of massive hosts suggests a stifled
production efficiency above ∼0.8 solar metallicity. The large dispersion
of the H-rich SLSNe host properties is in stark contrast to those of gamma-ray
burst, regular core-collapse SN, and H-poor SLSNe host galaxies. We propose
that multiple progenitor channels give rise to this sub-class