Sl(1|2) Super-Toda Fields

Abstract

Explicit exact solution of supersymmetric Toda fields associated with the Lie superalgebra 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 Drienfeld–Sokolov systems. 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 superalgebra osp(1|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 superalgebra, 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 superalgebras of the rank higher than 1.