  Recent advancements in the imaging of low-surface-brightness objects revealed
numerous ultra-diffuse galaxies in the local Universe. These peculiar objects
are unusually extended and faint: their effective radii are comparable to the
Milky Way, but their surface brightnesses are lower than that of dwarf
galaxies. Their ambiguous properties motivate two potential formation
scenarios: the "failed" Milky Way and the dwarf galaxy scenario. In this paper,
for the first time, we employ X-ray observations to test these formation
scenarios on a sample of isolated, low-surface-brightness galaxies. Since hot
gas X-ray luminosities correlate with the dark matter halo mass, "failed" Milky
Way-type galaxies, which reside in massive dark matter halos, are expected to
have significantly higher X-ray luminosities than dwarf galaxies, which reside
in low-mass dark matter halos. We perform X-ray photometry on a subset of
low-surface-brightness galaxies identified in the Hyper Suprime-Cam Subaru
survey, utilizing the XMM-Newton XXL North survey. We find that none of the
individual galaxies show significant X-ray emission. By co-adding the signal of
individual galaxies, the stacked galaxies remain undetected and we set an X-ray
luminosity upper limit of ${L_{\rm{0.3-1.2keV}}\leq6.2 \times 10^{37} (d/65
\rm{Mpc})^2 \ \rm{erg \ s^{-1}}}$ for an average isolated
low-surface-brightness galaxy. This upper limit is about 40 times lower than
that expected in a galaxy with a massive dark matter halo, implying that the
majority of isolated low-surface-brightness galaxies reside in dwarf-size dark
matter halos.
