By applying Noether method to $\mathcal{N}=1$ local supersymmetry in 11 dimensions, we obtained two candidates of $R^4$ corrections to the supergravity. The bosonic parts of these two completely match with the results obtained by type IIA string perturbative calculations. We also obtained 13 parameters which relate only fermionic terms.

• Received 23 January 2006

DOI:https://doi.org/10.1103/PhysRevD.74.025022