  We studied the optical counterpart of the intermediate-mass black hole
candidate HLX-1 in ESO 243-49. We used a set of Very Large Telescope imaging
observations from 2010 November, integrated by Swift X-ray data from the same
epoch. We measured standard Vega brightnesses U = 23.89 +/- 0.18 mag, B = 25.19
+/- 0.30 mag, V = 24.79 +/- 0.34 mag and R = 24.71 +/- 0.40 mag. Therefore, the
source was ~1 mag fainter in each band than in a set of Hubble Space Telescope
images taken a couple of months earlier, when the X-ray flux was a factor of 2
higher. We conclude that during the 2010 September observations, the optical
counterpart was dominated by emission from an irradiated disk (which responds
to the varying X-ray luminosity), rather than by a star cluster around the
black hole (which would not change). We modelled the Comptonized, irradiated
X-ray spectrum of the disk, and found that the optical luminosity and colours
in the 2010 November data are still consistent with emission from the
irradiated disk, with a characteristic outer radius r_{out} ~ 2800 r_{in} ~
10^{13} cm and a reprocessing fraction ~ 2 x 10^{-3}. The optical colours are
also consistent with a stellar population with age <~ 6 Myr (at solar
metallicity) and mass ~ 10^4 M_{sun}; this is only an upper limit to the mass,
if there is also a significant contribution from an irradiated disk. We
strongly rule out the presence of a young super-star-cluster, which would be
too bright. An old globular cluster might be associated with HLX-1, as long as
its mass <~ 2 x 10^6 M_{sun} for an age of 10 Gyr, but it cannot significantly
contribute to the observed very blue and variable optical/UV emission.
