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

Igor Bandos

doi:10.1007/jhep12(2019)106

Abstract

We present the complete supersymmetric and κ-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 κ-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 κsymmetry, 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 Stückelberg field for the 3-form gauge symmetry. This indicates that this symmetry is broken spontaneously by the superstring at the boundary of supermembrane.

Highlights

(SU(N ) SYM) theory and its effective description by Veneziano-Yankelovich (VY) action [23]
We present the complete supersymmetric and κ-symmetric action for the 4dimensional interacting system of open supermembrane, dynamical supergravity and 3form matter multiplets
We present the complete superfield action for such an interacting system and prove its κ-symmetry which is an important property indicating that the ground state of this dynamical system preserves a part of supersymmetry

Summary

Open supermembrane interacting with single 3-forms matter and supergravity

2.1 Supermembrane action in the background of 3-form supergravity and 3form matter. The action for a supermembrane in a supergravity background and in the background of supergravity and 3-form matter multiplet(s) can be written in the following form. Wess-Zumino term of the supermembrane action (2.1), C3 is the pullback of a 3-form potential defined in curved superspace and having the field strength 4-form expressed in terms of the above chiral superfield Z by. The form H4 is closed, dH4 = 0, when the supervielbein obeys the minimal supergravity constraints. The requirement that it is exact, i.e. that there exists a 3-form C3 Such that H4 = dC3, requires the chiral superfield Z to be special, namely to be constructed in terms of real superfield prepotential P = P∗, Z. There exists a residual gauge invariance with respect to additive transformations of real prepotential superfield P with real linear superfield L, δP = L , Dα Dα − R L = 0 , DαDα − R L = 0 Such transformation of the prepotential results in the gauge transformation of the superspace 3-form (2.9).

Supergravity interacting with closed supermembrane

Interaction with supergravity and single 3-form matter multiplet

Conclusion

A Torsion constraints of minimal supergravity

B Super-Weyl symmetry of the minimal supergravity constraints

C Useful equations on supermembrane worldvolume