  Recent detections of extremely short-timescale microlensing events imply the
existence of a large population of Earth- to Neptune-mass planets that appear
to have no host stars. However, it is currently unknown whether these objects
are truly free-floating planets or whether they are in wide orbits around a
distant host star. Here, we present an analysis of high-resolution imaging
observations of five free-floating planet candidates collected with the Keck
telescope. If these candidates were actually wide-orbit planets, then the light
of the host would appear at a separation of 40-60 mas from the microlensing
source star. No such stars are detected. We carry out injection and recovery
simulations to estimate the sensitivity to putative host stars at different
separations. Depending on the object, the presented observations rule out
11%-36\% of potential hosts assuming that the probability of hosting a planet
does not depend on the host mass. The results are sensitive to the latter
assumption, and the probability of detecting the host star in the analyzed
images may be a factor of 1.9 +/- 0.1 larger, if the exoplanet hosting
probability scales as the first power of the host star mass, as suggested by
recent studies of planetary microlensing events. We argue that deeper
observations, for example with JWST, are needed to confidently confirm or
refute the free-floating planet hypothesis.
