  We derive new constraints on the dilaton parameter appearing in the
spherically-symmetric black hole solution of Einstein-Maxwell-dilaton-axion
gravity, by studying the geodesic motion of the S2 star in the Galactic Center.
Einstein-Maxwell-dilaton-axion black holes represent a compelling alternative
to the standard black hole paradigm in General Relativity. This theory emerges
from the low energy effective action of the heterotic string theory and has
been proven to predict peculiar observational features from the direct imaging
of black hole shadows. At a fundamental level, Einstein-Maxwell-dilaton-axion
includes additional electromagnetic, dilatonic and axionic fields coupled to
the space-time metric. When considering charged non-rotating black hole
solutions, the additional fields endow the metric with one extra parameter $b$,
called dilaton parameter, that is theoretically bound to $0<b<M$. Using
publicly available astrometric data for S2 we derive an upper bound on
$b\lesssim 12M$ at 95% confidence level and we demonstrate that only including
the measurement of the relativistic orbital precession for S2 is sufficient to
reduce this bound to $b\lesssim 1.4M$ at the same confidence level.
Additionally, using a mock data mimicking future observations of S2 with the
GRAVITY interferometer, we show that improved astrometric precision can help
further narrow down the allowed dilaton parameter range to $b\lesssim0.033M$
after monitoring the S2 orbit for one and a half period.
