  The GES survey using FLAMES at the VLT has obtained high-resolution UVES
spectra for a large number of giant stars, allowing a determination of the
abundances of the key chemical elements C and N at their surface. The surface
abundances of these chemical species are well-known to change in stars during
their evolution on the red giant branch after the first dredge-up episod, as a
result of extra-mixing phenomena. We investigate the effects of thermohaline
mixing on C and N abundances using the first comparison between the GES [C/N]
determinations with simulations of the observed fields using a model of stellar
population synthesis. We explore the effects of thermohaline mixing on the
chemical properties of giants through stellar evolutionary models computed with
the stellar evolution code STAREVOL. We include these stellar evolution models
in the Besan\c{c}on Galaxy model to simulate the [C/N] distributions determined
from the UVES spectra of the GES and compare them with the observations.
Theoretical predictions including the effect of thermohaline mixing are in good
agreement with the observations. However, the field stars in the GES with C and
N-abundance measurements have a metallicity close to solar, where the
efficiency of thermohaline mixing is not very large. The C and N abundances
derived by the GES in open and globular clusters clearly show the impact of
thermohaline mixing at low-metallicity, allowing to explain the [C/N] ratio
observed in lower-mass and older giant stars. Using independent observations of
carbon isotopic ratio in clump field stars and open clusters, we also confirm
that thermohaline mixing should be taken into account to explain the behavior
of 12C/13C ratio as a function of stellar age. Overall the current model
including thermohaline mixing is able to reproduce very well the C- and
N-abundances over the whole metallicity range investigated by the GES data.
