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 Besanc{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.
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