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The Green-Schwarz formalism, or the superspace-formalism, are formalisms for supersymmetry with explicit spacetime supersymmetry.

The Green-Schwarz formalism, or the , are supersymmetry formalisms with explicit spacetime supersymmetry. The supersymmetric transformations on spacetime are (which is rather intuitive when compared with the RNS Worldsheet supersymmetry transformations) given by:

$$\begin{gathered} \delta {\Theta ^{Aa}} = {\varepsilon ^{Aa}} ; \\ \delta {X^\mu } = {{\bar \varepsilon }^A}{\gamma ^\mu }{\Theta ^A} ; \\ \end{gathered} $$

Then, the commutator of infinitesimal supersymmetric transformations yields:

$$ \begin{gathered} [{\delta _1},{\delta _2}]{X^\mu } = - 2\bar \varepsilon _1^A{\gamma ^\mu }\varepsilon _2^A = {a^\mu } \\ [{\delta _1},{\delta _2}]{\Theta ^A} = 0 \\ \end{gathered} $$

These transformations, combined with the ordinary Poincaré-transformations are called the Super-Poincaré transformations, the symmetry transformations of superspace.

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