How to make an action supersymmetric?

[yola]

Hello,

i am given an action (only scalars) and i want to make it supersymmetric. Any hints?
Do i simply add fermionic terms similar to those of the bosonic?

Thanks

 

[suprised]

No, in general there are restrictions on the bosonic interactions and you cannot supersymmetrize any given bosonic action by adding fermions. It is in general a non-trivial exercise.

 

[lpetrich]

For spin-0 scalar fields, one would add a spin-1/2 spinor field to each one to make a Wess-Zumino supersymmetric field (superfield). Since the on-shell numbers of bosonic and fermionic degrees of freedom must be equal, the scalar field must be a complex one.

Introductions to supersymmetry usually get into Wess-Zumino fields rather quickly, so it should not be much trouble to discover how to add superpartner fields.

 

[suprised]

Ineed not only the supermultiplet structure must work, but as said, there are restrictions on the bosonic interactions; not all scalar theories can be supersymmetrized. For example, a bosonic non-linear sigma model on some manifold M can only be supersymmetrized if M is a Kaehler manifold.

 

[Ben Niehoff]

The way this was traditionally done is by writing down the supersymmetry variations of all of your fields. Then see what happens to the action when you apply these SUSY variations. It will spit out some extra terms. So then you adjust your action and SUSY variations by adding more terms. Repeat this process until you don't have to add any more terms.

The whole thing is quite tedious, but that's how 11-dimensional SUGRA was found.

 

[yola]

Thanks