The Solution Construction Of Sl(2|1) SUSY Toda Model

Explicit exact solution of supersymmetric Toda field associated with the Lie super algebra sl(2|1) is constructed. The approach used is a super extension of Leznov-Saveliev algebraic analysis which is based on a pair of chiral and antichiral Drinfeld-Sokolov system. Though such approach is well understood for Toda field theories associated with ordinary Lie algebras, its super analogue was only successful in the super Liouville case with the underlying Lie super algebra osp(l|2). The problem lies in that a key step in the construction makes use of the tensor product decomposition of the highest weight representations of the underlying Lie super algebra which is not clear until recently. So our construction made in this paper presents a first explicit example of Leznov-Saveliev analysis for super Toda systems associated with underlying Lie super algebras of rank higher than 1.