Membranes and Three-form Supergravity

TL;DR

The paper constructs a fully off-shell, irreducible three-form version of $\mathcal{N}=1$ supergravity in four dimensions by dualizing auxiliary fields of old minimal supergravity and coupling to a constrained three-form multiplet. It then shows that κ-symmetric Green–Schwarz membranes require this three-form supergravity background, and derives both the elementary membrane solution (an AdS domain-wall) and the corresponding SUSY transformations. The authors demonstrate how the extended membrane superalgebra arises from the symmetries leaving the three-form background invariant, and contrast the flat-space extension with the AdS case where no central extension exists. Collectively, the work provides a detailed, off-shell framework for membranes in four-dimensional superspace and links dualization, gauge structure, and extended SUSY in a coherent formalism.

Abstract

We discuss membranes in four-dimensional N=1 superspace. The kappa-invariance of the Green-Schwarz action implies that there is a dual version of N=1 supergravity with a three-form potential. We formulate this new supergravity in terms of a three-form superfield in curved superspace, giving the relevant constraints on the field strength. We find the corresponding membrane soliton in the new supergravity and discuss how the extended supersymmetry algebra emerges from the symmetries of the flat superspace background.