Ifum 435/ft Quantum Symmetries in Supersymmetric Toda Theories

We consider two–dimensional supersymmetric Toda theories based on the Lie superalgebrasA(n, n), D(n+1, n) and B(n, n) which admit a fermionic set of simple roots and a fermionic untwisted affine extension. In particular, we concentrate on two simple examples, the B(1, 1) and A(1, 1) theories. Both in the conformal and massive case we address the issue of quantum integrability by constructing the first non trivial conserved currents and proving their conservation to all–loop orders. While the D(n+1, n) and B(n, n) systems are genuine N = 1 supersymmetric theories, the A(n, n) models possess a global N = 2 supersymmetry. In the conformal case, we show that the A(n, n) stress–energy tensor, uniquely determined by the holomorphicity condition, has vanishing central charge and it corresponds to the stress–energy tensor of the associated topological theory. Invited talk at the International Workshop “String theory, quantum gravity and the unification of the fundamental interactions” Roma – September 1992 IFUM 435/FT November 1992