We conducted the first long-term (60 d), multiwavelength (optical, ultraviolet, UV, and X-ray) simultaneous monitoring of
Cen X-4 with daily Swift observations from 2012 June to August, with the goal of understanding variability in the low-mass
X-ray binary Cen X-4 during quiescence. We found Cen X-4 to be highly variable in all energy bands on time-scales from days
to months, with the strongest quiescent variability a factor of 22 drop in the X-ray count rate in only 4 d. The X-ray, UV
and optical (V band) emission are correlated on time-scales down to less than 110 s. The shape of the correlation is a power
law with index γ about 0.2-0.6. The X-ray spectrum is well fitted by a hydrogen neutron star (NS) atmosphere (kT = 59-80 eV)
and a power law (with spectral index Γ = 1.4-2.0), with the spectral shape remaining constant as the flux varies. Both components
vary in tandem, with each responsible for about 50 per cent of the total X-ray flux, implying that they are physically linked.
We conclude that the X-rays are likely generated by matter accreting down to the NS surface. Moreover, based on the short
time-scale of the correlation, we also unambiguously demonstrate that the UV emission cannot be due to either thermal emission
from the stream impact point, or a standard optically thick, geometrically thin disc. The spectral energy distribution shows
a small UV emitting region, too hot to arise from the accretion disc, that we identified as a hotspot on the companion star.
Therefore, the UV emission is most likely produced by reprocessing from the companion star, indeed the vertical size of the
disc is small and can only reprocess a marginal fraction of the X-ray emission. We also found the accretion disc in quiescence
to likely be UV faint, with a minimal contribution to the whole UV flux.