Recent questions tagged superspace-formalism The Green-Schwarz formalism, or the Superspace formalism are supersymmetry formalisms with explicit spacetime supersymmetry. The supersymmetric transformations on spacetime are (which is rather intuitive if you compare this to the RNS Worldsheet supersymmetry transformations) given by:

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

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 poincaire-transformations are called the Super-Poincaire transformations, the symmetry transformations of superspace.

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