  Aims. We search for low-mass companions in the innermost region (<300 mas,
i.e., 6 AU) of the beta Pic planetary system. Methods. We obtained
interferometric closure phase measurements in the K-band with the VLTI/AMBER
instrument used in its medium spectral resolution mode. Fringe stabilization
was provided by the FINITO fringe tracker. Results. In a search region of
between 2 and 60 mas in radius, our observations exclude at 3 sigma
significance the presence of companions with K-band contrasts greater than 5e-3
for 90% of the possible positions in the search zone (i.e., 90% completeness).
The median 1-sigma error bar in the contrast of potential companions within our
search region is 1.2e-3. The best fit to our data set using a binary model is
found for a faint companion located at about 14.4 mas from beta Pic, which has
a contrast of 1.8e-3 \pm 1.1e-3 (a result consistent with the absence of
companions). For angular separations larger than 60 mas, both time smearing and
field-of-view limitations reduce the sensitivity. Conclusions. We can exclude
the presence of brown dwarfs with masses higher than 29 Mjup (resp. 47 Mjup) at
a 50% (resp. 90%) completeness level within the first few AUs around beta Pic.
Interferometric closure phases offer a promising way to directly image low-mass
companions in the close environment of nearby young stars.
