Formally Renormalizable Gravitationally Self Interacting String Models

It has recently been shown how the effect of the divergent part of the gravitational self interaction for a classical string model in 4 dimensions can be allowed for by a renormalisation of its stress energy tensor and in the elastic case a corresponding renormalisation of the off shell action. It is shown here that that it is possible to construct a new category of elastic string models for which this effect is describable as a renormalisation in the stricter “formal” sense, meaning that it only requires a rescaling of one of the fixed parameters characterising the model.