Superfield equations for the interacting system of D=4 N=1 supermembrane and scalar multiplet

We present the superfield action for the dynamical N=1 D=4 supermembrane in interaction with a dynamical scalar multiplet and use it to derive the superfield equations of motion. These include the supermembrane equations, which formally coincide with equations of supermembrane in a background of the (off-shell) scalar multiplet, and the special chiral superfield equations with supermembrane source. In the case when the scalar supermultiplet part of the action contains only the simplest kinetic term we have also extracted the spacetime component field equations from the superfield equations and solve these in the leading order on supermembrane tension. The inclusion of nontrivial superpotential and relation with known supersymmetric domain wall solutions is briefly discussed.Comment: 26 pages. V2: misprints corrected, references and an acknowledgment added, minor changes, in particular in sec. 4.2.1. V.3. discussion on the relation with known solutions added; to appear in Nucl.Phys. B (2011

Three form potential in (special) minimal supergravity superspace and supermembrane supercurrent

This contribution begins the study of the complete superfield Lagrangian description of the interacting system of D=4 N=1 supergravity (SUGRA) and supermembrane. Firstly, we review a 'three form supergravity' by Ovrut and Waldram, which we prefer to call 'special minimal supergravity'. This off-shell formulation of simple SUGRA is appropriate for our purposes as the supermembrane action contains the so-called Wess-Zumino term given by the integral over a three form potential in superspace, C3. We describe this formulation in the frame of Wess--Zumino superfield approach, showing how the basic variations of minimal SUGRA are restricted by the conditions of the existence of a three-form potential C3 in its superspace. In this language the effect of dynamical generation of cosmological constant, known to be characteristic for this formulation of SUGRA, appears in its superfield form, first described by Ogievetsky and Sokatchev in their formulation of SUGRA as a theory of axial vector superfield. Secondly, we vary the supermembrane action with respect to the special minimal SUGRA superfields (basic variations) and obtain the supercurrent superfields as well as the supergravity superfield equations with the supermembrane contributions.Comment: 18 pages, no figures. V2: Important references added. The abstract and presentation have been changed to reflect the overloop with that. Submitted to the QTS7 Proceedings. J. Phys. style use

Supermembrane interaction with dynamical D=4 N=1 supergravity. Superfield Lagrangian description and spacetime equations of motion

We obtain the complete set of equations of motion for the interacting system of supermembrane and dynamical D=4 N = 1 supergravity by varying its complete superfield action and writing the resulting superfield equations in the special gauge where the supermembrane Goldstone field is set to zero. We solve the equations for auxiliary fields and discuss the effect of dynamical generation of cosmological constant in the Einstein equation of interacting system and its renormalization due to some regular contributions from supermembrane. These two effects (discussed in late 70th and 80th, in the bosonic perspective and in the supergravity literature) result in that, generically, the cosmological constant has different values in the branches of the spacetime separated by the supermembrane worldvolume.Comment: 23 pages, no figures. V2 two references added, 24 page

Extended supersymmetry in massless conformal higher spin theory

We propose superfield equations in tensorial N-extended superspaces to describe the N=2,4,8 supersymmetric generalizations of free conformal higher spin theories. These can be obtained by quantizing a superparticle model in N-extended tensorial superspace. The N-extended higher spin supermultiplets just contain scalar and 'spinor' fields in tensorial space so that, in contrast with the standard (super)space approach, no nontrivial generalizations of the Maxwell or Einstein equations to tensorial space appear when N>2. For N=4,8, the higher spin-tensorial components of the extended tensorial superfields are expressed through additional scalar and spinor fields in tensorial space which obey the same free higher spin equations, but that are axion-like in the sense that they possess Peccei-Quinn-like symmetries.Comment: 0ne reference added; to appear in Nucl. Phys. B. 18 pages, plain late