The supermembrane revisited

TL;DR

The paper develops a comprehensive superembedding treatment of the M2-brane, deriving its dynamics, κ-symmetry, and worldvolume conformal supergeometry from the embedding constraint. It then shows that gauging a target-space U(1) isometry yields the D2-brane in Type IIA supergravity, with the Dirac-Born-Infeld action arising from a gauged Wess-Zumino construction and the RR 1-form gauging aligning with IIA fields. Extending to massive backgrounds, the authors lift to a massive D=11/IIA framework, deriving the modified torsion, Wess-Zumino terms, and a D2-brane action that includes a Chern-Simons term proportional to the mass. Collectively, the work unifies M2 dynamics, D2-brane physics, and their massive extensions within a covariant superembedding formalism and KK reduction, clarifying the induced worldvolume supergeometry and action principles.

Abstract

The M2-brane is studied from the perspective of superembeddings. We review the derivation of the M2-brane dynamics and the supergravity constraints from the standard superembedding constraint and we discuss explicitly the induced d=3, N=8 superconformal geometry on the worldvolume. We show that the gauged supermembrane, for a target space with a U(1) isometry, is the standard D2-brane in a type IIA supergravity background. In particular, the D2-brane action, complete with the Dirac-Born-Infeld term, arises from the gauged Wess-Zumino worldvolume 4-form via the brane action principle. The discussion is extended to the massive D2-brane considered as a gauged supermembrane in a massive D=11 superspace background. Type IIA supergeometry is derived using Kaluza-Klein techniques in superspace.