Supersymmetrizing bosonic actions at higher orders 
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*Given only the bosonic terms of a supersymmetric action, using a knowledge of the (local) supersymmetry transformations, is there a systematic way of reconstructing the fermionic terms?

*More generally, if higher order bosonic terms are added to the action with unknown coefficients, how can one use the knowledge of the original SUGRA transformations + the fact that the original action was supersymmetric, to compute these coefficients? I don't see how this is possible without also knowing the extra fermionic terms that these higher order bosonic terms spawn.
 A: *

*Yes, there is systematic way called the Noether procedure. Simply you write down all possible 2-derivative fermionic terms with arbitrary coefficients and vary the action using the SUSY transformation rules. Then, you fix the coefficients to obtain the invariance up to a total derivative.

*When you have 4-derivatives, there are two cases:
a. Off-Shell SUSY: In this case, if the theory has superconformal symmetry, then you can use superconformal tensor calculus. If not, then use off-shell superspace. In the worst case scenario, you can once again write down all possible bosonic and fermionic terms and vary the action using the off-shell transformation rules. You need to fix the arbitraray coefficients to get invariance up to a total derivative.
b. On-Shell SUSY: In this case, you have to modify the action as well as the transformation rules. This is because the on-shell supersymmetry means that the transformation rules form a closed algebra when the field equations are imposed. This one is quite tedious, and the procedure is again the Noether procedure. I do not think you want to go into this one. 
