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

Abstract

Abstract: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 "WZθ =0 " gauge where the supermembrane Goldstone field is set to zero (θ = 0). 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.

Three-forms in supergravity and flux compactifications

“…It is well known that different off-shell formulations of four-dimensional N = 1 supergravity can be obtained from its superconformal version by choosing different compensator fields [47][48][49]. Here the use of Y as a compensator in the super-Weyl-invariant formulation leads, as was shown in [35], to the three-form minimal supergravity [8,[13][14][15]32,33], in which the imaginary part of the old minimal auxiliary field M is substituted by the Hodge dual of a real field strength…”

Higher Forms and Membranes in 4D Supergravities

“…in [37][38][39][40][41][58][59][60], membranes can indeed be promoted to objects moving in the whole four-dimensional superspace. In particular, a kappa-symmetric world-volume action describing the coupling of a supermembrane to a variant of minimal N = 1 supergravity with a single gauge three-form field was considered in [37,40,41] and a kappa-symmetric action for a supermembrane coupled to a single three-form chiral matter superfield in flat N = 1 superspace was constructed in [39]. A space-time component action describing the interaction of a membrane with supergravity and scalar matter multiplets, in which the membrane part of the action is purely bosonic, was considered in [38].…”

“…where G d is the real vector superfield of minimal supergravity satisfying D˙α G αα = D α R. [66] When T is identified with the chiral compensator of a Weyl transformation of the superconformally invariant formulation of supergravity, the above action describes the supermembrane interacting with three-form variants of pure minimal supergravity. [60] In particular, if P is a generic real scalar superfield one deals with the single three-form supergravity and arrives at the action of [37,41] upon gauge fixing T = 1. While, if P is the real part of a complex linear superfield the membrane is coupled to the double three-form supergravity 2 .…”

“…Supersymmetric models of variant threeform multiplets have been studied in a series of publications [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] and couplings with supersymmetric membranes have been also investigated. [37][38][39][40][41][42] These fields generically will arise from type-II string compactifications on Calabi-Yau manifolds with fluxes [8,13,43,44] and can thus provide the realization of the aforementioned physical scenarios in effective four-dimensional supergravity models. Interestingly, for variant matter three-form chiral multiplets, the non-zero expectation values of * F 4 fluxes may induce spontaneous supersymmetry breaking and generate a positive contribution to the cosmological constant.…”

“…This formulation can also be extracted from the equations in[41], although there it was not described in detail.…”