N=1 D=4 supermembrane in the coset approach

TL;DR

This paper develops a nonlinear realization framework for the N=1 D=4 supermembrane and its dual super D2-brane, constructing invariant actions and exploring their geometric and supersymmetry-breaking properties.

Contribution

It introduces a novel approach using nonlinear realizations to describe supermembranes and super D2-branes, including their duality and geometric interpretation of equations of motion.

Findings

Constructed invariant off-shell Goldstone superfield actions.

Demonstrated duality between supermembrane and super D2-brane actions.

Provided geometric interpretation of superfield equations of motion.

Abstract

$N=1 D=4$ supermembrane (in a flat background) and super D2-brane dual to it are described within the nonlinear realizations approach as theories of the partial supersymmetry breaking $N=1 D=4 \to N=1 d=3$. We construct the relevant invariant off-shell Goldstone superfield actions and demonstrate them to be dual to each other. Their bosonic cores are, respectively, the static-gauge Nambu-Goto and $d=3$ Born-Infeld actions. The supermembrane superfield equation of motion admits a transparent geometric interpretation suggesting an extension of the standard superembedding constraints. We briefly discuss the 1/4 breaking of $N=1 D=5$ supersymmetry along similar lines.