Note on embedding of M-theory corrections into eleven-dimensional superspace

By analyzing eleven-dimensional superspace fourth-rank superfield strength F-Bianchi identities, we show that M-theory corrections to eleven-dimensional supergravity cannot be embedded into the mass dimension zero constraints, such as the (γ^ab)_αβX_ab^c or i(γ^a₁⋯a₅)_αβX_a1⋯a5^c terms in the supertorsion constraint T_αβ^c. The only possible modification of the superspace constraint at dimension zero is found to be the scaling of F_αβcd like F_αβcd=(1/2)(γ_cd)_αβe^Φ for some real scalar superfield Φ, which alone is further shown not to embed general M-theory corrections enough. This conclusion is based on the dimension zero F-Bianchi identity under the two assumptions: (i) There are no negative dimensional constraints on the F-superfield strength, F_αβγδ=F_αβγd=0; (ii) the supertorsion T-Bianchi identities and F-Bianchi identities are not modified by Chern-Simons terms. Our result can serve as a powerful tool for future exploration of M-theory corrections embedded into eleven-dimensional superspace supergravity.