Conformally invariant field theories in two dimensions critical systems and strings

The author presents a study of conformally invariant field theories from the double view point of string theories and critical systems unravelled as an interesting structure. The string theories discussed here at not based on free field theories in two dimensions and, hence, the dual amplitudes are difficult to determine. The common feature of all the new conformally invariant field theories discussed here is the appearance of operators of dimension 1. For the associated string theories, it corresponds to the existence of a massless string state. This fact should play a key role in the complete understanding of these models. On the other hand, the relevance of these new models to particle physics is not yet clear. The supersymmetric version of the present discussion has been worked out in all details