Studying molecular species in protoplanetary disks is very useful to characterize the properties of these objects, which are the site of planet formation. We attempt to constrain the chemistry of S-bearing molecules in the cold parts of circumstellar disk of GG Tau A. We searched for H$_2$S, CS, SO, and SO$_2$ in the dense disk around GG Tau A with the NOrthem Extended Millimeter Array (NOEMA) interferometer. We detected H$_2$S emission from the dense and cold ring orbiting around GG Tau A. This is the first detection of H$_2$S in a protoplanetary disk. We also detected HCO$^+$, H$^{13}$CO$^+$, and DCO$^+$ in the disk. Upper limits for other molecules, CCS, SO$_2$, SO, HC$_3$N, and $c$-C$_3$H$_2$ are also obtained. The observed DCO$^+$/HCO$^+$ ratio is similar to those in other disks. The observed column densities, derived using our radiative transfer code DiskFit, are then compared with those from our chemical code Nautilus. The column densities are in reasonable agreement for DCO$^{+}$, CS, CCS, and SO$_2$. For H$_2$S and SO, our predicted vertical integrated column densities are more than a factor of 10 higher than the measured values. Our results reinforce the hypothesis that only a strong sulfur depletion may explain the low observed H$_2$S column density in the disk. The H$_2$S detection in GG Tau A is most likely linked to the much larger mass of this disk compared to that in other T Tauri systems.
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