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

We present an algebraic derivation of the supersymmetry flow transformations for the relativistic sector of the extended mKdV hierarchy. The deduction relies in the introduction of Fermionic Lax operators constructed from an algebraic Dressing method underlying an extended Riemann-Hilbert problem for Affine Kac-Moody superalgebras with a half-integer gradation. A generalized set of relativistic local Fermionic conservation laws is introduced and it is shown that the simplest one, corresponding to the lowest Isospectral times t±1 and non-Abelian flows t ±1/2 , provides the supercharges generating the usual supersymmetry transformations in 2D superspace. The number of supercharges is equal to the dimension of the Fermionic kernel of a given semisimple element E ∈ b 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 work out in detail.