D=3, N=8 conformal supergravity and the Dragon window

We give a superspace description of D=3, N=8 supergravity. The formulation is off-shell in the sense that the equations of motion are not implied by the superspace constraints (but an action principle is not given). The multiplet structure is unconventional, which we connect to the existence of a "Dragon window", that is modules occurring in the supercurvature but not in the supertorsion. According to Dragon's theorem this cannot happen above three dimensions. We clarify the relevance of this window for going on the conformal shell, and discuss some aspects of coupling to conformal matter.Comment: plain tex, 24 pp v2: minor change

N=2 Conformal Superspace in Four Dimensions

We develop the geometry of four dimensional N=2 superspace where the entire conformal algebra of SU(2,2|2) is realized linearly in the structure group rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries, extending to N=2 our prior result for N=1 superspace. This formulation explicitly lifts to superspace the existing methods of the N=2 superconformal tensor calculus; at the same time the geometry, when degauged to SL(2,C) x U(2)_R, reproduces the existing formulation of N=2 conformal supergravity constructed by Howe.Comment: 43 pages; v2 references added, acknowledgments update

Variant supercurrent multiplets

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.Comment: 11 pages; V2: minor changes in sect. 3; V3: published version; V4: typos in eq. (2.3) corrected; V5: comments and references adde

N=2 supergravity and supercurrents

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 constant non-vanishing real isotriplet g^{ij}=g^{ji} which originates as an expectation value of the tensor compensator. Upon reduction to N=1 superfields, we show that the model describes two dually equivalent formulations for the massless multiplet (1,3/2)+(3/2,2) depending on a choice of g^{ij}. In the case g^{11}=g^{22}=0, the action describes (i) new minimal N=1 supergravity; and (ii) the Fradkin-Vasiliev-de Wit-van Holten gravitino multiplet. In the case g^{12}=0, on the other hand, the action describes (i) old minimal N=1 supergravity; and (ii) the Ogievetsky-Sokatchev gravitino multiplet.Comment: 40 pages; v2: added references, some comments, new appendi

Pure spinor superfields -- an overview

Maximally supersymmetric theories do not allow off-shell superspace formulations with traditional superfields containing a finite set of auxiliary fields. It has become clear that off-shell supersymmetric action formulations of such models can be achieved by the introduction of pure spinors. In this talk, an overview of this formalism is given, with emphasis on D=10 super-Yang-Mills theory and D=11 supergravity. This a somewhat expanded version of a talk presented at the workshop "Breaking of supersymmetry and ultraviolet divergences in extended supergravity" (BUDS), Laboratori Nazionali di Frascati, March 25-28, 2013.Comment: 34 pp., 2 figs., contributions to the proceedings of the workshop "Breaking of supersymmetry and ultraviolet divergences in extended supergravity" (BUDS), Laboratori Nazionali di Frascati, March 25-28, 201

Extended supersymmetric sigma models in AdS_4 from projective superspace

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.Comment: 88 pages; v3: typos corrected, version published in JHE

Sigma models with off-shell N=(4,4) supersymmetry and noncommuting complex structures

We describe the conditions for extra supersymmetry in N=(2,2) supersymmetric nonlinear sigma models written in terms of semichiral superfields. We find that some of these models have additional off-shell supersymmetry. The (4,4) supersymmetry introduces geometrical structures on the target-space which are conveniently described in terms of Yano f-structures and Magri-Morosi concomitants. On-shell, we relate the new structures to the known bi-hypercomplex structures.Comment: 20 pages; v2: significant corrections, clarifications, and reorganization; v3: discussion of supersymmetry vs twisted supersymmetry added, relevant signs corrected

Ectoplasm with an Edge

The construction of supersymmetric invariant actions on a spacetime manifold with a boundary is carried out using the "ectoplasm" formalism for the construction of closed forms in superspace. Non-trivial actions are obtained from the pull-backs to the bosonic bodies of closed but non-exact forms in superspace; finding supersymmetric invariants thus becomes a cohomology problem. For a spacetime with a boundary, the appropriate mathematical language changes to relative cohomology, which we use to give a general formulation of off-shell supersymmetric invariants in the presence of boundaries. We also relate this construction to the superembedding formalism for the construction of brane actions, and we give examples with bulk spacetimes of dimension 3, 4 and 5. The closed superform in the 5D example needs to be constructed as a Chern-Simons type of invariant, obtained from a closed 6-form displaying Weil triviality.Comment: 25 page

The linear multiplet and ectoplasm

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 potential not annihilated by the central charge (unlike the standard N=2 vector multiplet). Such a gauge one-form can be chosen to describe a variant nonlinear vector-tensor multiplet. As a byproduct of our construction, we also find a variant realization of the tensor multiplet in supergravity where one of the auxiliaries is replaced by the field strength of a gauge three-form.Comment: 31 pages; v3: minor corrections and typos fixed, version to appear in JHE

Six-dimensional Supergravity and Projective Superfields

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.Comment: 39 pages; v3: some modifications in section 2; equations (2.3), (2.14b), (2.16) and (2.17) correcte