In N = 1 rigid supersymmetric theories, there exist three standard realizations of the supercurrent multiplet corresponding to the (i) old minimal, (ii) new minimal and (iii) non-minimal off-shell formulations for N = 1 supergravity. Recently, Komargodski and Seiberg in arXiv:1002.2228 put forward a new supercurrent and proved its consistency, although in the past it was believed not to exist. In this paper, three new variant supercurrent multiplets are proposed. Implications for supergravity-matter systems are discussed.
Theories with 3D $\mathcal{N}=2$ bulk supersymmetry may preserve a 2D $\mathcal{N}=(0,2)$ subalgebra when a boundary is introduced, possibly with localized degrees of freedom. We propose generalized supercurrent multiplets with bulk and boundary parts adapted to such setups. Using their structure, we comment on implications for the $\overline{Q}_+$-cohomology. As an example, we apply the developed framework to Landau-Ginzburg models. In these models, we study the role of boundary degrees of freedom and matrix factorizations. We verify our results using quantization.
Correlators of gauge invariant operators provide useful information on the dynamics, phases and spectra of a quantum field theory. In this paper, we consider N=1 supersymmetric theories and focus our attention on the supercurrent multiplet. We give a complete characterization of two-point functions of operators belonging to such multiplet, like the energy-momentum tensor and the supercurrent, and study the relations between them. We discuss instances of weakly coupled and strongly coupled theories, in which different symmetries, like conformal invariance and supersymmetry, may be conserved and…
We consider the minimal off-shell formulation for four-dimensional N=2 supergravity with a cosmological term, in which the second compensator is an improved tensor multiplet. We use it to derive a linearized supergravity action (and its dual versions) around the anti-de Sitter (AdS) background in terms of three N=2 off-shell multiplets: an unconstrained scalar superfield, vector and tensor multiplets. This allows us to deduce the structure of the supercurrent multiplet associated with those supersymmetric theories which naturally couple to the supergravity formulation chosen, with or without a…
Non-conformal supercurrents in six dimensions are described, which contain the trace of the energy-momentum tensor and the gamma-trace of the supersymmetry current amongst their component fields. Within the superconformal approach to ${\cal N} = (1, 0)$ supergravity, we present various distinct non-conformal supercurrents, one of which is associated with an ${\cal O}(2)$ (or linear) multiplet compensator, while another with a tensor multiplet compensator. We also derive an infinite class of non-conformal supercurrents involving ${\cal O}(n)$ multiplets with $n > 2$. As an illustrative example …
We analyze various supersymmetry multiplets containing the supercurrent and the energy-momentum tensor. The most widely known such multiplet, the Ferrara-Zumino (FZ) multiplet, is not always well-defined. This can happen once Fayet-Iliopoulos (FI) terms are present or when the Kahler form of the target space is not exact. We present a new multiplet S which always exists. This understanding of the supersymmetry current allows us to obtain new results about the possible IR behavior of supersymmetric theories. Next, we discuss the coupling of rigid supersymmetric theories to supergravity. When th…
Supersymmetric field theories possess a rich structure in their supercurrent supermultiplets. Some symmetries are manifest in one supercurrent supermultiplet but not in the others; for instance, R-symmetry is manifest in the R-multiplet but not in the Ferrara-Zumino multiplet. Similarly, we argue that dilatation symmetry is manifest in the Virial multiplet (also known as a variant minimal supercurrent supermultiplet in the literature). It reveals that R-symmetry and dilatation symmetry are conceptually independent without further assumptions even though the superconformal symmetry connects the…
We address the problem of classifying all N=2 supercurrent multiplets in four space-time dimensions. For this purpose we consider the minimal formulation of N=2 Poincare supergravity with a tensor compensator, and derive its linearized action in terms of three N=2 off-shell multiplets: an unconstrained scalar superfield, a vector multiplet, and a tensor multiplet. Such an action was ruled out to exist in the past. Using the action constructed, one can derive other models for linearized N=2 supergravity by applying N=2 superfield duality transformations. The action depends parametrically on a c…
We discuss local supercurrents as sources of the super-Einstein equations in the superconformal approach in the old and new minimal (auxiliary fields) formulation. Modifications of the Ward identity giving the covariant divergence of the Einstein multiplet are considered in presence of a Fayet-Iliopoulos term. Curvature multiplets can be used as alternative to the gravitino variation in the search for rigid supersymmetric curved backgrounds.
Consistent supercurrent multiplets are naturally associated with linearized off-shell supergravity models. In arXiv:1002.4932 we presented the hierarchy of such supercurrents which correspond to all the models for linearized 4D N = 1 supergravity classified a few years ago. Here we analyze the correspondence between the most general supercurrent given in arXiv:1002.4932 and the one obtained eight years ago in hep-th/0110131 using the superfield Noether procedure. We apply the Noether procedure to the general N = 1 supersymmetric nonlinear sigma-model and show that it naturally leads to the so-…
We systematically analyze all possible supersymmetry multiplets that include the supersymmetry current and the energy-momentum tensor in various dimensions, focusing on N=1 in four dimensions. The most general such multiplet is the S-multiplet, which includes 16 bosonic and 16 fermionic operators. In special situations it can be decomposed, leading to smaller multiplets with 12+12 or even 8+8 operators. Physically, these multiplets give rise to different brane charges in the supersymmetry algebra. The S-multiplet is needed when the algebra contains both string and domain wall charges. In lower…
Long ago, Achucarro and Townsend discovered that in three dimensions (3D) N-extended anti-de Sitter (AdS) supergravity exists in several incarnations, which were called the (p,q) AdS supergravity theories with non-negative integers p>=q such that N=p+q. Using the superspace approach to 3D N-extended supergravity developed in arXiv:1101.4013, we present three superfield formulations for N=2 supergravity that allow for well defined cosmological terms and supersymmetric AdS solutions. The conformal compensators corresponding to these theories are respectively: (i) a chiral scalar multiplet: (ii) …
Recently, Komargodski and Seiberg have proposed a new type of supercurrent multiplet which contains the energy-momentum tensor and the supersymmetry current consistently. In this paper we study quantum properties of the supercurrent in renormalizable field theories. We point out that the new supercurrent gives a quite simple resolution to the classic problem, called the anomaly puzzle, that the Adler-Bardeen theorem applied to an R-symmetry current is inconsistent with all order corrections to $β$ functions. We propose an operator equation for the supercurrent in all orders of perturbation the…
We continue the program of constructing cubic interactions between matter and higher spin supermultiplets. In this work we consider a complex linear superfield and we find that it can have cubic interactions only with supermultiplets with propagating spins $j=s+1$, $j=s+1/2$ for any non-negative integer $s$ (half-integer superspin supermultiplets). We construct the higher spin supercurrent and supertrace, these compose the canonical supercurrent multiplet which generates the cubic interactions. We also prove that for every $s$ there exist an alternative minimal supercurrent multiplet, with van…
The Noether currents associated with the non-linearly realized super-Poincare' symmetries of the Green-Schwarz (Nambu-Goto-Akulov-Volkov) action for a non-BPS p=2 brane embedded in a N=1, D=4 target superspace are constructed. The R symmetry current, the supersymmetry currents, the energy-momentum tensor and the scalar central charge current are shown to be components of a world volume supercurrent. The centrally extended superconformal transformations are realized on the Nambu-Goldstone boson and fermion fields of the non-BPS brane. The superconformal currents form supersymmetry multiplets wi…
In four spacetime dimensions there exist two off-shell formulations for the massless multiplet of superspin $(s+\frac 12)$, where $s=2,3, \dots$. These supersymmetric higher spin gauge theories, known as longitudinal and transverse, are dual to each other and describe two massless fields of spin $(s+\frac 12)$ and $(s+1)$ upon elimination of the auxiliary fields. They respectively reduce, in the limiting case of $s=1$, to the linearised actions for the old minimal and the $n=-1$ non-minimal ${\cal N}=1$ supergravity theories. Associated with these gauge massless theories are non-conformal high…
Starting from the 48+48 component multiplet of supercurrents for a rigid N=2 tensor multiplet in four spacetime dimensions, we obtain the transformation of the linearized supergravity multiplet which couples to this supercurrent multiplet. At the linearized level, this 48+48 component supergravity multiplet decouples into the 24+24 component linearized standard Weyl multiplet and a 24+24 component irreducible matter multiplet containing a real scalar field. By a consistent application of the supersymmetry algebra with field dependent structure constants appropriate to N=2 conformal supergravit…
In a classical conformal invariant supersymmetric gauge theory, the chiral R-symmetry current, the supersymmetry current and the energy-momentum tensor constitute a supercurrent multiplet. There are two different superconformal anoamly multiplets in four-dimensional supersymmetric gauge theories, one originating from the supersymmetric gauge dynamics and the consequent nonvanishing β-function, and the other one coming from the coupling of the supercurrent multiplet to the external supergravity multiplet with non-trivial topology. We emphasize that in the gauge/gravity dual correspondence these…
We determine the general structure of quantum anomalies for the $R$-multiplet of four dimensional $\mathcal{N}=1$ supersymmetric quantum field theories in the presence of background fields for an arbitrary number of Abelian flavor multiplets. By solving the Wess-Zumino consistency conditions for off-shell new minimal supergravity in four dimensions with an arbitrary number of Abelian vector multiplets, we compute the anomaly in the conservation of the supercurrent to leading non trivial order in the gravitino and vector multiplet fermions. We find that both $R$-symmetry and flavor anomalies ne…
We revisit the supermultiplet structure of Noether currents for N=1 supersymmetric gauge theories. Using superfield identities and the field equations we show how to derive a superfield equation for the divergences of the Noether currents in terms of the supercurrent and anomaly superfields containing 16_B+16_F components. We refer to this as the natural supercurrent structure as it is invariant under all local symmetries of the theory. It corresponds to the S-multiplet of Komargodski and Seiberg. We clarify the on/off-shell nature of the currents appearing in this multiplet and we study in de…
We propose higher spin supercurrent multiplets for ${\cal N}=1$ supersymmetric field theories in four-dimensional anti-de Sitter space (AdS). Their explicit realisations are derived for various supersymmetric theories, including a model of $N$ massive chiral scalar superfields with an arbitrary mass matrix. We also present new off-shell gauge formulations for the massless ${\cal N}=1$ supersymmetric multiplet of integer superspin $s$ in AdS, where $s =2,3,\dots$, as well as for the massless gravitino multiplet (superspin $s=1$) which requires special consideration.
In this paper,hidden sectors of Ferrara-Zumino multiplets with contributions to soft terms coming from quantum supergravity are investigated in framework of gravity mediation. The two-point correlator of Ferrara-Zumino multiplets can be parameterized, which implies the wave function renormalizations of components fields in gravity supermultiplet can be evaluated in relatively simple form. Soft terms are calculated via supercurrent approach. We find gaugino masses are independent of sfermion masses on general grounds. The unification of gaugino masses is not universal. In comparison with genera…
We develop a general formalism to study the three-point correlation functions of conserved higher-spin supercurrent multiplets $J_{α(r) \dotα(r)}$ in 4D ${\cal N}=1$ superconformal theory. All the constraints imposed by ${\cal N}=1$ superconformal symmetry on the three-point function $\langle J_{α(r_1) \dotα(r_1)} J_{β(r_2) \dotβ(r_2) }J_{γ(r_3) \dotγ(r_3)}\rangle$ are systematically derived for arbitrary $r_1, r_2, r_3$, thus reducing the problem mostly to computational and combinatorial. As an illustrative example, we explicitly work out the allowed tensor structures contained in $\langle J_…
We investigate cubic interactions between a chiral superfield and higher spin superfield corresponding to irreducible representations of the $4D,\, \mathcal{N}=1$ super-Poincaré algebra. We do this by demanding an invariance under the most general transformation, linear in the chiral superfield. Following Noether's method we construct an infinite tower of higher spin supercurrent multiplets which are quadratic in the chiral superfield and include higher derivatives. The results are that a single, massless, chiral superfield can couple only to the half-integer spin supermultiplets $(s+1,s+1/2)$…
This thesis presents the general structure of non-conformal higher-spin supercurrent multiplets in three and four spacetime dimensions. Such supercurrents are in one-to-one correspondence with off-shell massless higher-spin gauge supermultiplets, some of which are constructed in this thesis for the first time. In the first part of the thesis, we propose a new off-shell formulation for a massless integer superspin multiplet, whose gauge-invariant action involves an unconstrained complex superconformal prepotential, in conjunction with two types of compensators. Next, we deduce the structure of …
Boundary conditions in supergravity on a manifold with boundary relate the bulk gravitino to the boundary supercurrent, and the normal derivative of the bulk metric to the boundary energy-momentum tensor. In the 3D N=1 setting, we show that these boundary conditions can be stated in a manifestly supersymmetric form. We identify the Extrinsic Curvature Tensor Multiplet, and show that boundary conditions set it equal to (a conjugate of) the boundary supercurrent multiplet. Extension of our results to higher-dimensional models (including the Randall-Sundrum and Horava-Witten scenarios) is discuss…
In this paper the variant supercurrents based on consistency and completion in off-shell N=1 supergravity are studied. We formulate the embedding relations for supersymmetric current and energy tensor into supercurrent multiplet. Corresponding linearized supergravity is obtained with appropriate choice of Wess-Zumino gauge in each gravity supermultiplet.
We study supersymmetry breaking in theories with non-minimal multiplets (such as the complex linear or CNM multiplets), by using superspace higher derivative terms which give rise to new supersymmetry breaking vacuum solutions on top of the standard supersymmetric vacuum. We illustrate the decoupling of the additional massive sectors inside the complex linear and the CNM multiplets and show that only the Goldstino sector is left in the low energy limit. We also discuss the duality between non-minimal scalar multiplets and chiral multiplets in the presence of superspace higher derivatives. From…
The recent paper arXiv:1205.6881 has developed superform formulations for two versions of the vector-tensor multiplet and their Chern-Simons couplings in four-dimensional N = 2 conformal supergravity. One of them is the standard vector-tensor multiplet with the central charge gauged by a vector multiplet. The other is the variant vector-tensor multiplet with the property that its own one-form gauges the central charge. Here a more general setup is presented in which the known versions reside as special cases. Analysis of the setup demonstrates that under certain assumptions there are two disti…
We construct the supercurrent multiplet that contains the energy-momentum tensor of the (2,0) tensor multiplet. By coupling this multiplet of currents to the fields of conformal supergravity, we first construct the linearized superconformal transformations rules of the (2,0) Weyl multiplet. Next, we construct the full non-linear transformation rules by gauging the superconformal algebra OSp(8^*|4). We then use this result to construct the full equations of motion of the tensor multiplet in a conformal supergravity background. Coupling N+5 copies of the tensor multiplet to conformal supergravit…
In this paper, we study the general form of three-point functions of conserved current multiplets $S_{α(k)}= S_{(α_1 \dots α_k)}$ of arbitrary rank in four-dimensional ${\mathcal N}=1$ superconformal theory. We find that the correlation function of three such operators $\langle \bar{S}_{\dotα(k)} (z_1) S_{β(k+l)} (z_2) \bar{S}_{\dotγ(l)} (z_3) \rangle$ is fixed by the superconformal symmetry up to a single complex coefficient though the precise form of the correlator depends on the values of $k$ and $l$. In addition, we present the general structure of mixed correlators of the form $\langle \b…
For general N=5 and N=6 superconformal field theories in three dimensions, we compute the three-point correlation functions of the supercurrent multiplets. In each case, N=5 and N=6, the functional form of this correlator is uniquely fixed modulo an overall coefficient which is related, by superconformal Ward identities, to the parameter in the two-point function of the supercurrent. The structure of the correlation functions obtained is consistent with the property that every N=5 superconformal field theory, considered as a special N=4 theory, is invariant under the mirror map.
We describe several families of primary linear supermultiplets coupled to three-dimensional ${\cal N}=2$ conformal supergravity and use them to construct topological $BF$-type terms. We introduce conformal higher-spin gauge superfields and associate with them Chern-Simons-type actions that are constructed as an extension of the linearised action for ${\cal N}=2$ conformal supergravity. These actions possess gauge and super-Weyl invariance in any conformally flat superspace and involve a higher-spin generalisation of the linearised ${\cal N}=2$ super-Cotton tensor. For massless higher-spin supe…
We analyse Feynman diagram calculational issues related to the quantum breaking of supercurrent conservation in a supersymmetric non-abelian Yang-Mills theory. For the sake of simplicity, we take a zero mass gauge field multiplet interacting with a massless Majorana spin-$1/2$ field in the adjoint representation of $SU(2)$. We shed light on a long-standing controversy regarding the perturbative evaluation of the supercurrent anomaly in connection with gauge and superconformal symmetry in different frameworks. We find that only superconformal symmetry is unambiguously broken using an invariant …
In the framework of the superconformal tensor calculus for 4D N=2 supergravity, locally supersymmetric actions are often constructed using the linear multiplet. We provide a superform formulation for the linear multiplet and derive the corresponding action functional using the ectoplasm method (also known as the superform approach to the construction of supersymmetric invariants). We propose a new locally supersymmetric action which makes use of a deformed linear multiplet. The novel feature of this multiplet is that it corresponds to the case of a gauged central charge using a one-form potent…
We consider mixed three-point correlation functions of the supercurrent and flavour current in three-dimensional $1 \leq \mathcal{N} \leq 4$ superconformal field theories. Our method is based on the decomposition of the relevant tensors into irreducible components to guarantee that all possible tensor structures are systematically taken into account. We show that only parity even structures appear in the correlation functions. In addition to the previous results obtained in arXiv:1503.04961, it follows that supersymmetry forbids parity odd structures in three-point functions involving the supe…
By utilizing a new procedure (the RADIO method) for deriving on-shell 2D, 2N-extended multiplets from off-shell 2D, N-extended multiplets, we derive a new on-shell 2D, N = 8 representation; the ultra-multiplet. By twisting with respect to parity, we show that many variant versions of this supermultiplet also exist.
We construct the dilaton Weyl multiplet for $N=2$ conformal supergravity in four dimensions. Beginning from an on-shell vector multiplet coupled to the standard Weyl multiplet, the equations of motion can be used to eliminate the supergravity auxiliary fields, following a similar pattern as in five and six dimensions. The resulting 24+24 component multiplet includes two gauge vectors and a gauge two-form and provides a variant formulation of $N=2$ conformal supergravity. We also show how this dilaton Weyl multiplet is contained in the minimal 32+32 Poincare supergravity multiplet introduced by…
We present a variant formulation of N=1 supersymmetric compensator mechanism for an arbitrary non-Abelian group in four dimensions. This formulation resembles our previous variant supersymmetric compensator mechanism in 4D. Our field content consists of the three multiplets: (i) A Non-Abelian Yang-Mills multiplet (A_μ^I, λ^I, C_{μνρ}^I), (ii) a tensor multiplet (B_{μν}^I, χ^I, φ^I) and an extra vector multiplet (K_μ^I, ρ^I, C_{μνρ}^I) with the index I for the adjoint representation of a non-Abelian gauge group. The C_{μνρ}^I is originally an auxiliary field dual to the conventional auxiliary f…
The concept of self-dual supersymmetric nonlinear electrodynamics is generalized to a curved superspace of N = 1 supergravity, for both the old minimal and the new minimal versions of N = 1 supergravity. We derive the self-duality equation, which has to be satisfied by the action functional of any U(1) duality invariant model of a massless vector multiplet, and construct a family of self-dual nonlinear models. This family includes a curved superspace extension of the N = 1 super Born-Infeld action. The supercurrent and supertrace in such models are proved to be duality invariant. The most inte…
The recent papers arXiv:1110.0971 and arXiv:1201.5431 have provided a superfield description for vector-tensor multiplets and their Chern-Simons couplings in 4D N = 2 conformal supergravity. Here we develop a superform formulation for these theories. Furthermore an alternative means of gauging the central charge is given, making use of a deformed vector multiplet, which may be thought of as a variant vector-tensor multiplet. Its Chern-Simons couplings to additional vector multiplets are also constructed. This multiplet together with its Chern-Simons couplings are new results not considered by …
We construct the fermionic sector and supersymmetry transformation rules of a variant N=(1,1) supergravity theory obtained by generalized Kaluza-Klein reduction from seven dimensions. We show that this model admits both (Minkowski)_4 x S^2 and (Minkowski)_3 x S^3 vacua. We perform a consistent Kaluza-Klein reduction on S^2 and obtain D=4, N=2 supergravity coupled to a vector multiplet, which can be consistently truncated to give rise to D=4, N=1 supergravity with a chiral multiplet.
We propose a nilpotent ${\cal N}=1$ tensor multiplet describing two fields, which are the Goldstino and the axion, the latter being realised in terms of the field strength of a gauge two-form. This supersymmetric multiplet is formulated in terms of a deformed real linear superfield, subject to a cubic nilpotency condition. Its couplings to a super Yang-Mills multiplet and supergravity are presented. To define a nilpotent tensor multiplet in the locally supersymmetric case, one has to make use of either real or complex three-form supergravity theories, which are variant realisations of the old …
When a globally supersymmetric theory is scale invariant, it must possess a Virial supercurrent supermultiplet. The multiplet structure is analogous to the R-current supermultiplet in globally R-symmetric theories but we put extra "$i$"s in various formulae. We construct a novel type of supergravity from gauging the Virial supercurrent supermultiplet in $d=1+3$ dimensions. We give the full non-linear superspace action with the help of a covariantly linear unitary superconformal compensator. The resulting supergravity is peculiar: (1) no Einstein-like second order kinetic term is allowed withou…
We present a new (variant) formulation of N=1 supersymmetric compensator mechanism for an arbitrary non-Abelian group in four dimensions. We call this `variant supersymmetric non-Abelian Proca-Stueckelberg formalism'. Our field content is economical, consisting only of the two multiplets: (i) A Non-Abelian vector multiplet (A_μ^I, λ^I, C_{μνρ}{}^I) and (ii) A compensator tensor multiplet (B_{μν}{}^I, χ^I, φ^I). The index I is for the adjoint representation of a non-Abelian gauge group. The C_{μνρ}{}^I is originally an auxiliary field Hodge-dual to the conventional auxiliary field D^I. The φ^I …
Within the framework of (2,0) anti-de Sitter (AdS) supersymmetry in three dimensions, we propose a multiplet of higher-spin currents. Making use of this supercurrent, we construct two off-shell gauge formulations for a massless multiplet of half-integer superspin $(s+\frac 12)$, for every integer $s>0$. In the $s=1$ case, one formulation describes the linearised action for (2,0) anti-de Sitter supergravity, while the other gives the type III minimal supergravity action in (2,0) AdS superspace, with both linearised supergravity actions originally derived in arXiv:1109.0496. The constructed mass…
For N-extended superconformal field theories in three spacetime dimensions (3D), with N=1,2,3, we compute the two- and three-point correlation functions of the supercurrent and the flavour current multiplets. We demonstrate that supersymmetry imposes additional restrictions on the correlators of conserved currents as compared with the non-supersymmetric case studied by Osborn and Petkou in hep-th/9307010. It is shown that the three-point function of the supercurrent is determined by a single functional form consistent with the conservation equation and all the symmetry properties. Similarly, t…
We investigate the "$T\bar{T}$" deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the $T\bar{T}$ deforming operator can be constructed as a supersymmetric descendant. Here we focus on $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ supersymmetry. As an example, we analyse in detail the $T\bar{T}$ deformation of a free $\mathcal{N}=(1,0)$ supersymmetric action. We also argue that the link between $T\bar{T}$ and string theory can be extended to superstrings: by analysing the light-c…
We formulate $\mathcal{N}=2$ global supersymmetric Lagrangians of self-interacting vector multiplets in terms of variant multiplets, whose non-propagating fields are replaced with gauge three-forms. Setting the three-forms on-shell results in a dynamical generation of the parameters entering the scalar potential. As an application, we study how gauge three-forms may determine the partial breaking of $\mathcal{N}=2$ supersymmetry and how they affect the low energy effective description.
We argue that off-shell dualities between d=1 supermultiplets with different sets of physical bosonic components and the same number of fermionic ones are related to gauging some symmetries in the actions of the supermultiplets with maximal sets of physical bosons. Our gauging procedure uses off-shell superfields and so is manifestly supersymmetric. We focus on N=4 supersymmetric mechanics and show that various actions of the multiplet (3,4,1) amount to some gauge choices in the gauged superfield actions of the linear or nonlinear (4,4,0) multiplets. In particular, the conformally invariant (3…
We propose a superspace formulation of N=(1,0) conformal supergravity in six dimensions. The corresponding superspace constraints are invariant under super-Weyl transformations generated by a real scalar parameter. The known variant Weyl super-multiplet is recovered by coupling the geometry to a super-3-form tensor multiplet. Isotwistor variables are introduced and used to define projective superfields. We formulate a locally supersymmetric and super-Weyl invariant action principle in projective superspace. Some families of dynamical supergravity-matter systems are presented.
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 $V \to {\rm e}^τV$, where $τ$ is an arbitrary real scalar superfield. We next propose a ne…
