INTEGRABLE SYSTEMS AND 2-LOOP ALGEBRAS IN STRING THEORY

The entire theory of strings in the first-quantized formalism cannot be exhausted by the theory of conformal models. It is hardly possible to restrict oneself to the addition to it of only two-dimensional integrable systems. However, the study of such systems can prove to be useful for future generalizations. A universal formulation of all conformal and integrable models should be the first step in this program. Some steps in this direction are discussed in the framework of the Lagrangian approach. The main conclusion is that there is a need to study two-loop algebras (generated, for example, by quantum fields on two-dimensional complex surfaces) and their quantum deformations.