Supercurrents and superconformal symmetry

We develop a superspace Noether procedure for supersymmetric field theories in 4-dimensions for which an off-shell formulation in ordinary superspace exists. In this way we obtain an elegant and compact derivation of the various supercurrents in these theories. We then apply this formalism to compute the central charges for a variety of effective actions. As a by-product we also obtain a simple derivation of the anomalous superconformal Ward-identity in N=2 Yang-Mills theory. The connection with linearized supergravity is also discussed.Comment: 47 pages, Latex, improved pedagogical presentation and references adde

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“…This suggests that the supercurrent is just the one for the Wess-Zumino model, (3.19), but with derivatives replaced by covariant ones [16]:…”

Section: Supersymmetric Qedmentioning

confidence: 97%

Superfield Noether Procedure

Magro¹,

Sachs²,

Wolf³

2002

Annals of Physics

102

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“…This coincides with the general supercurrent derived eight years ago by Magro, Sachs and Wolf [19] with the aid of a modification of the superfield Noether procedure elaborated in [20] (see also [21]), provided the operators V and U are globally well-defined scalar superfields. However, for such operators V and U , the supercurrent (8) proves to be equivalent to the Ferrara-Zumino one.…”

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confidence: 99%

Variant supercurrents and Noether procedure

Kuzenko

2011

Eur. Phys. J. C

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Consistent supercurrent multiplets are naturally associated with linearized off-shell supergravity models. In S.M. Kuzenko, J. High Energy Phys. 1004, 022 (2010 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 S.M. Kuzenko, J. High Energy Phys. 1004, 022 (2010 and the one obtained eight years ago in M. Magro et al., Ann. Phys. 298, 123 (2002) 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-called S-multiplet, revitalized in Z. Komargodski, N. Seiberg, J. High Energy Phys. 1007, 017 (2010).Inspired by a recent work of Komargodski and Seiberg [1], we have presented in [2] the hierarchy of supercurrent multiplets which are associated with the models for linearized 4D N = 1 supergravity classified several years ago in [3]. The most general form of such a multiplet is as follows:Here J αα =J αα denotes the supercurrent, while the chiral superfields χ α , η α and X constitute the so-called multiplet of anomalies. The conservation law (1) incorporates six smaller supercurrent multiplets, of which three include 12 + 12 operators (minimal supercurrents) and the rest describe 16 + 16 components (reducible multiplets). Let us recall the structure of the minimal supercurrent multiplets. The casea e-mail: kuzenko@cyllene.uwa.edu.au describes the famous Ferrara-Zumino multiplet [4]. It corresponds to the old minimal formulation for N = 1 supergravity [5][6][7]. Another choice,corresponds to the new minimal supergravity [8,9] (this supercurrent was studied in [10][11][12]). The third choice,corresponds to the minimal 12 + 12 supergravity formulation which was proposed a few years ago in [13]. Unlike the old minimal and the new minimal theories, this formulation is known at the linearized level only. Among the three reducible supercurrents with 16 + 16 components [2], the most interesting multiplet 1 is singled out by the conditionIt corresponds to the model (36) in [3], which can be shown to be a linearized version of the so-called 16 + 16 supergravity [14,15] known to be reducible [16]. After a 'death sentence' given to this multiplet in the late 1970s, it was recently resurrected by Komargodski and Seiberg [1]. These authors postulated the following supercurrent conservation law:and proved, using laborious component calculations, its consistency in the sense that J αα contains a conserved energymomentum tensor and a conserved supersymmetry current.1 The other reducible supercurrents are obtained by setting either χ α = 0 or X = 0. They appear to be less interesting than the one defined by (5), because the corresponding supergravity formulations are known at the linearized level only.

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“…However, since we are aiming at future applications to brane-world physics, a more pragmatic course is chosen here, which is based on the introduction of the relevant superconformal Killing vectors and elaborating associated building blocks. The concept of superconformal Killing vectors [28,29,30,31,32,21,33], has proved to be extremely useful for various studies of superconformal theories in four and six dimensions, see e.g. [34,35,36].…”

Section: Introductionmentioning

confidence: 99%

On compactified harmonic/projective superspace, 5D superconformal theories, and all that

Kuzenko

2006

Nuclear Physics B

160

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Within the supertwistor approach, we analyse the superconformal structure of 4D N = 2 compactified harmonic/projective superspace. In the case of 5D superconformal symmetry, we derive the superconformal Killing vectors and related building blocks which emerge in the transformation laws of primary superfields. Various off-shell superconformal multiplets are presented both in 5D harmonic and projective superspaces, including the so-called tropical (vector) multiplet and polar (hyper)multiplet. Families of superconformal actions are described both in the 5D harmonic and projective superspace settings. We also present examples of 5D superconformal theories with gauged central charge.

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Supercurrents and superconformal symmetry

Cited by 22 publications

References 22 publications

Superfield Noether Procedure

Superfield Noether Procedure

Variant supercurrents and Noether procedure

On compactified harmonic/projective superspace, 5D superconformal theories, and all that

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