POSSIBLE IMPLICATIONS OF INTEGRABLE SYSTEMS FOR STRING THEORY

A kind of program for the unification of conformal and two-dimensional integrable models is described. Integrable systems, defined by the condition of vanishing curvature (Lax representation), can be derived from universal generalizations of Wess-Zumino-Witten action, including one more integration (over spectral parameter lambda). Such actions, in their turn, should be derivable from some membrane-like action, related to the Kirillov-Kostant form for some quantum two-loop Lie algebras (like complexification of Fairlie's deformed algebra of two-dimensional area-preserving reparametrizations).