ON THE STABILITY OF THE DILATON MEAN FIELD
The extension of study done in a previous work about the dilaton mean field stabilization thanks to the potential generated by massive fermions, is reviewed. Three loop corrections were evaluated in addition to the previously calculated two loop terms. The results indicate that the dilaton vacuum field tend to be fixed at a high value close to the Planck scale, in accordance with the need for predicting Einstein gravity from string theory. Moreover, the mass of the dilaton is evaluated to be also a high value close to the Planck mass, which implies the absence of dilaton scalar signals in modern cosmological observations. These properties arise when the fermion mass is chosen to be either at a lower bound corresponding to the top quark mass, or alternatively, at a very much higher value assumed to be in the grand unification energy range.