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Register a new userComplex three-form supergravity and membranes
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There exist two variants of the old minimal formulation for ${cal N}=1$ supergravity in four dimensions, in which one or each of the two auxiliary scalars is replaced by the field strength of a gauge three-form. These theories are known as three-form supergravity and complex three-form supergravity, respectively. For each of them, we present a super-Weyl invariant coupling of supergravity to the supermembrane and prove kappa-invariance of the resulting action. In the case of three-form supergravity, we demonstrate that the action constructed reduces to that given by Ovrut and Waldram twenty years ago upon imposing a super-Weyl gauge in which the compensating three-form superfield is set to a constant.
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We develop off-shell formulations for ${cal N}=1$ and ${cal N}=2$ anti-de Sitter supergravity theories in three spacetime dimensions that contain gauge two-forms in the auxiliary field sector. These formulations are shown to allow consistent couplings of supergravity to the Green-Schwarz superstring with ${cal N}=1$ or ${cal N}=2$ spacetime supersymmetry. In addition to being $kappa$-symmetric, the Green-Schwarz superstring actions constructed are also invariant under super-Weyl transformations of the target space. We also present a detailed study of models for spontaneously broken local supersymmetry in three dimensions obtained by coupling the known off-shell ${cal N}=1$ and ${cal N}=2$ supergravity theories to nilpotent Goldstino superfields.
By using integral forms we derive the superspace action of D=3, N=1 supergravity as an integral on a supermanifold. The construction is based on target space picture changing operators, here playing the role of Poincare duals to the lower-dimensional spacetime surfaces embedded into the supermanifold. We show how the group geometrical action based on the group manifold approach interpolates between the superspace and the component supergravity actions, thus providing another proof of their equivalence.
We consider superconformal field theories in three and six dimensions with eight supercharges which can be realized on the world-volume of M-theory branes sitting at orbifold singularities. We find that they should admit a N=4 and N=2 supergravity dual in AdS_4 and AdS_7, respectively. We discuss the characteristics of the corresponding gauged supergravities.
The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein-Hilbert term with cosmological constant, the gravitational sector contains the Lorentz-Chern-Simons form and a term involving the torsion each with arbitrary couplings. The supersymmetric extension is carried out for vanishing and negative effective cosmological constant, and it is shown that the action can be written as a Chern-Simons theory for the supersymmetric extension of the Poincare and AdS groups, respectively. The construction can be simply carried out by making use of a duality map between different gravity theories discussed here, which relies on the different ways to make geometry emerge from a single gauge potential. The extension for N =p+q gravitini is also performed.
Recently, a nilpotent real scalar superfield $V$ was introduced in arXiv:1702.02423 as a model for the Goldstino. It contains only two independent component fields, the Goldstino and the auxiliary $D$-field. Here we first show that $V$ can equivalently be realised as a constrained three-form superfield. We demonstrate that every irreducible Goldstino superfield (of which the Goldstino is the only independent component field) can be realised as a descendant of $V$ which is invariant under local rescalings $V to {rm e}^tau V$, where $tau$ is an arbitrary real scalar superfield. We next propose a new Goldstino supermultiplet which is described by a nilpotent three-form superfield $cal Y$ that is a variant formulation for the nilpotent chiral superfield, which is often used in off-shell models for spontaneously broken supergravity. It is shown that the action describing the dynamics of $cal Y$ may be obtained from a supersymmetric nonlinear $sigma$-model in the infrared limit. Unlike $V$, the Goldstino superfield $cal Y$ contains two independent auxiliary fields, $F= H+{rm i} G$, of which $H$ is a scalar and $G$ is the field strength of a gauge three-form. When $cal Y$ is coupled to supergravity, both $H$ and $G$ produce positive contributions to the cosmological constant. While the contribution from $H$ is uniquely determined by the parameter of the supersymmetry breaking in the action, the contribution from $G$ is dynamical.
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