A Note on Embedding of M-Theory Corrections into Eleven-Dimensional Superspace

TL;DR

This paper investigates the constraints on embedding M-theory corrections into eleven-dimensional superspace supergravity, concluding that only limited modifications are possible under certain assumptions, thus guiding future research directions.

Contribution

It demonstrates that M-theory corrections cannot be embedded into standard superspace constraints at dimension zero, except for a specific scalar superfield scaling, under particular assumptions.

Findings

M-theory corrections cannot be embedded into dimension zero constraints.

The only modification is a scalar superfield scaling of F_{ ext{a} ext{b} ext{c} ext{d}}.

Additional modifications require relaxing certain assumptions.

Abstract

By analyzing eleven-dimensional superspace fourth-rank superfield strength F-Bianchi identities, we show that M-theory corrections to eleven-dimensional supergravity can not be embedded into the mass dimension zero constraints, such as the (\g^{a b})_{\a\b} X_{a b}{}^c or i (\g^{a_1... a_5})_{\a\b} X_{a_1... a_5}{}^c -terms in the supertorsion constraint T_{\a\b}{}^c. The only possible modification of superspace constraint at dimension zero is found to be the scaling of F_{\a\b c d} like F_{\a\b c d} = (1/2) \big(\g_{c d}\big)_{\a\b} e^\Phi for some real scalar superfield \Phi, which alone is further shown not enough to embed general M-theory corrections. 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_{\a\b\g\d} = F_{\a\b\g d} =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.