In super yang mills theories in 4,6,10 dimensions, the supersymmetry transformation is often written as (ignoring color indices):(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \delta A_\mu = i \bar \alpha \gamma_\mu \lambda - i \bar \lambda \gamma_\mu \alpha [/tex]

[tex] \delta \lambda = c F^{\mu \nu} [ \gamma_\mu, \gamma_\nu] \alpha [/tex]

where c is some constant depending on dimension, and [itex]\alpha[/itex] is the parameter of the transformation, a fermionic c-number spinor.

I have a few questions about this. First of all, are we supposed to assume [itex]\alpha[/itex] has the same properties as [itex]\lambda[/itex], ie, wrt majorana and weyl -ness? It seems like we should to get the right number of supercharges, and maybe to preserve the corresponding property of [itex]\lambda[/itex] after a transformation, but this is never mentioned.

Second, what exactly do these transformations mean in terms of the susy generators Q? Do these generators fit into a spinor with the same properties as [itex]\alpha[/itex] and [itex]\lambda[/itex]? If so, and if we call this spinor Q, can we write:

[tex] \delta \mathcal{O} = [ \bar \alpha Q, \mathcal{O} ] [/tex]

This doesn't seem right, because if [itex]\alpha[/itex] is Weyl, the RHS doesn't depend on the conjugates of Q. Maybe it's something like:

[tex] \delta \mathcal{O} = [ \bar \alpha Q + \bar Q \alpha, \mathcal{O} ] [/tex]

Is this right? And in any case, what would be the easiest way to determine the anticommutators of the Q's given the transformations in the form of the first equations above?

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# Supersymmetry notation question

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