Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy

[摘要] We couple two copies of the supersymmetric mKdV hierarchy by means of the algebraic dressing technique. This allows to deduce the whole set of ( N , N ) supersymmetry transformations of the relativistic sector of the extended mKdV hierarchy and to interpret them as fermionic symmetry flows. The construction is based on an extended Riemann-Hilbert problem for affine Kac-Moody superalgebras with a half-integer gradation. A generalized set of relativistic-like fermionic local current identities is introduced and it is shown that the simplest one, corresponding to the lowest isospectral times t ±1 provides the supercharges generating rigid supersymmetry transformations in 2D superspace. The number of supercharges is equal to the dimension of the fermionic kernel of a given semisimple element E ∈ ^g which defines both, the physical degrees of freedom and the symmetries of the model. The general construction is applied to the N =(1,1) and N =(2,2) sinh-Gordon models which are worked out in detail.

[关键词] algebraic dressing method;supersymmetry flows;supersymmetric af fine Toda models