11-dimensional curved backgrounds for supermembrane in superspace

Abstract

We compute part of the superfield in terms of the component fields of 11-dimensional on-shell supergravity by using `Gauge completion' in 2nd-order formalism. The result is the same as was derived recently in 1.5-order formalism by B. de Wit, K. Peeters and J. Plefka. We use 2nd-order formalism because in order to hold $κ$-invariance generally 2nd-order formalism is more hopeful and simpler than 1.5-order formalism.