sl(1|2) Super-Toda Fields |
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Authors: | YANG Zhan-Ying XUE Pan-Pan ZHAO Liu SHI Kang-Jie |
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Institution: | 1. Department of Physics, Northwest University, Xi'an 710069, China
;2. Department of Physics, Nankai University, Tianjin 300071, China
;3. Institute of Modern Physics, Northwest University, Xi'an 710069, China |
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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. |
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Keywords: | Toda field supersymmetry exact solution |
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