  We report on the galaxy MACSJ0032-arc at z=3.6314 discovered during the
Herschel Lensing snapshot Survey of massive galaxy clusters, and strongly
lensed by the cluster MACSJ0032.1+1808. The successful detections of its
rest-frame UV, optical, FIR, millimeter, and radio continua, and of its CO
emission enable us to characterize, for the first time at such a high redshift,
the stellar, dust, and molecular gas properties of a compact star-forming
galaxy with a size smaller than 2.5 kpc, a fairly low stellar mass of 4.8x10^9
Msun, and a moderate IR luminosity of 4.8x10^11 Lsun. We find that the bulk of
the molecular gas mass and star formation seems to be spatially decoupled from
the rest-frame UV emission. About 90% of the total star formation rate is
undetected at rest-frame UV wavelengths because of severe obscuration by dust,
but is seen through the thermal FIR dust emission and the radio synchrotron
radiation. The observed CO(4-3) and CO(6-5) lines demonstrate that high-J
transitions, at least up to J=6, remain excited in this galaxy, whose CO
spectral line energy distribution resembles that of high-redshift submm
galaxies, even though the IR luminosity of MACSJ0032-arc is ten times lower.
This high CO excitation is possibly due to the compactness of the galaxy. We
find evidence that this high CO excitation has to be considered in the balance
when estimating the CO-to-H2 conversion factor. The inferred depletion time of
the molecular gas in MACSJ0032-arc supports the decrease in the gas depletion
timescale of galaxies with redshift, although to a lesser degree than predicted
by galaxy evolution models. Instead, the measured molecular gas fraction as
high as 60-79% in MACSJ0032-arc favors the continued increase in the gas
fraction of galaxies with redshift as expected, despite the plateau observed
between z~1.5 and z~2.5.
