Field Theory on Noncommutative Space-Time and the Deformed Virasoro Algebra

Abstract

We consider a field theoretical model on the noncommutative cylinder which leads to a discrete-time evolution. Its Euclidean version is shown to be equivalent to a model on the complex $q$-plane. We reveal a direct link between the model on a noncommutative cylinder and the deformed Virasoro algebra constructed earlier on an abstract mathematical background. As it was shown, the deformed Virasoro generators necessarily carry a second index (in addition to the usual one), whose meaning, however, remained unknown. The present field theoretical approach allows one to ascribe a clear meaning to this second index: its origin is related to the noncommutativity of the underlying space-time. The problems with the supersymmetric extension of the model on a noncommutative super-space are briefly discussed.