  Searches for planetary transits carried out in open and globular clusters
have yielded to date only a handful of weak, unconfirmed candidates. These
results have been interpreted either as being insignificant, or as evidence
that the cluster chemical or dynamical environment inhibits the planetary
formation or survival. Most campaigns were limited by small sample statistics
or systematics from ground-based photometry. In this work we performed a search
for transiting planets and variables in a deep stellar field of NGC 6397 imaged
by HST-ACS for 126 orbits. We analyzed 5,078 light curves, including a pure
sample of 2,215 cluster-member M0-M9 dwarfs. The light curves have been
corrected for systematic trends and inspected with several tools. No
high-significance planetary candidate is detected. We compared this null
detection with the most recent results from Kepler, showing that no conclusive
evidence of lower planet incidence can be drawn. However, a very small
photometric jitter is measured for early-M cluster members (<~2 mmag on 98% of
them), which may be worth targeting in the near future with more optimized
campaigns. Twelve variable stars are reported for the first time.
