Quantum conserved currents in supersymmetric Toda theories

Abstract

We consider N = 1 supersymmetric Toda theories which admit a fermionic untwisted affine extension, i.e. the systems based on the A( n, n), D( n + 1, n) and B( n, n) superalgebras. We construct the superspace Miura transformations which allow us to determine the W-supercurrents of the conformal theories and we compute their renormalized expressions. The analysis of the renormalization and conservation of higher-spin currents in then performed for the corresponding supersymmetric massive theories. We establish the quantum integrability of these models and show that although their lagrangian is not hermitian, the masses of the fundamental particles are real, a property which is maintained by one-loop corrections. The spectrum is actually much richer, since the theories admit solitons. The existence of quantum conserved higher-spin charges implies that elastic, factorized S-matrices can be constructed.