In supergravity models with low supersymmetry breaking scale the gravitinos can be superlight , with mass in the 10 ^ { -6 } eV to few keV range .
In such a case , gravitino emission provides a new cooling mechanism for protoneutron stars and therefore can provide constraints on the mass of a superlight gravitino .
This happens because the coupling to matter of superlight gravitinos is dominated by its goldstino component , whose coupling to matter is inversely proportional to the scale of supersymmetry breaking and inceases as the gravitino mass decreases .
Present observations therefore provide lower limits on the gravitino mass .
Using the recently revised goldstino couplings , we find that the two dominant processes in supernova cooling are e ^ { + } e ^ { - } \rightarrow \tilde { G } \tilde { G } and \gamma + e ^ { - } \rightarrow e ^ { - } \tilde { G } \tilde { G } .
They lead to a lower limit on the supersymmetry breaking scale \Lambda _ { S } from 160 to 500 GeV for core temperatures 30 to 60 MeV and electron chemical potentials 200 to 300 MeV .
The corresponding lower limits on the gravitino mass are .6 - 6 \times 10 ^ { -6 } eV .