Superstring at the boundary of open supermembrane interacting with D=4 supergravity and matter supermultiplets

TL;DR

This paper constructs a complete supersymmetric and kappa-symmetric action for an open supermembrane interacting with 4D supergravity and matter multiplets, revealing partial supersymmetry preservation and spontaneous symmetry breaking at the boundary.

Contribution

It provides the first complete formulation of an open supermembrane coupled to supergravity and matter, including boundary terms and symmetry analysis.

Findings

Boundary term acts as a superstring action.

Kappa-symmetry imposes two projection conditions.

Supersymmetry preserved is at most 1/4 in ground states.

Abstract

We present the complete supersymmetric and $\kappa$--symmetric action for the 4-dimensional interacting system of open supermembrane, dynamical supergravity and 3--form matter multiplets. The cases of a single 3-form matter multiplet and a quite generic model with a number of nonlinear interacting double 3-form multiplets are considered. In all cases the fermionic parameter of the $\kappa$-symmetry is subject to two apparently different projection conditions which suggests that the ground state of the system, in particular a domain junction, might preserve at most 1/4 of the spacetime supersymmetry. The boundary term of the open supermembrane action, needed to preserve the $\kappa$-symmetry, has the meaning of the action of a superstring. The Wess--Zumino term of this superstring action is expressed in terms of real linear superfield playing the role of St\"uckelberg field for the 3--form gauge symmetry. This indicates that this symmetry is broken spontaneously by the superstring at the boundary of supermembrane.