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A part of the supersymmetry algebra is $$\{Q_a,~{\bar Q}_{\dot b}\}~=~-2i\sigma^\mu_{a\dot b}\partial_\mu$$ which is a momentum operator $p_\mu~=~-i\partial_\mu$. The graded Lie algebra $g~=~h~+~k$ $$[h,~h]~\subset~h,~[h,~k]~\subset~k,~\{k,~k\}~\subset~h,$$ where the last of these contains the above anti-commutator. This model has chiral symmetry. It ...